The paper discusses an optical layout for obtaining reduced X-ray oblique images, which can be useful for X-ray lithography problems. A special feature of the layout is the ability to illuminate the photomask at small grazing angles while recording images with minimal distortion. Using numerical simulations carried out for an X-ray laser with an operating wavelength of 13.9 nm, the spatial resolution and field of view of this system are found.

One of the tasks of modern optical methods is the most complete description of the objects under study and the wave fields. For example, properties of the materials under study should be characterized not only by absorption but also by refraction, and the wave fields behind the object and near the detector should be characterized not only by intensity but also by phase. The work of Gerchberg and Saxton in 1972 was the first attempt to accomplish this task without using any optical elements, relying only on a quadratic detector and a computer simulation of the propagation of electromagnetic waves. Today, similar lensless imaging methods are applied across a wide range of wavelengths—from terahertz to hard X-ray. The purpose of this paper is to provide a brief introduction to the theory of lensless methods as applied to the X-ray wavelength range. It also presents the results of recent experiments on lensless imaging of test objects conducted at the Lebedev Physical Institute using lasers.

Improving the efficiency and expanding the scope of application of lensless optics require increasing its reliability in measuring light fields. The paper examines the complex field generated by a phase object, i.e., a lens. It is shown that reliable phase reconstruction is possible using two or more measurements of the intensity distribution at different distances from the object. A combination of a circular diaphragm and a lens located behind it is used as an object.

Ptychography today is considered the most natural and effective method for approaching the diffraction limit of optical resolution. The principal scheme of a ptychoscope does not contain refractive or focusing elements and includes a coherent light source, a platform for moving (macroscopic) object, and a detector for registering radiation passed through or reflected by the object associated with a computer for processing diffraction patterns. In classical optics, the main task in achieving high spatial resolution is the correction and elimination of aberrations of optical systems, while in ptychography spatial resolution mainly depends on the reliability of registration and computer processing of diffraction patterns with large numerical apertures. The key idea of ptychography is to obtain an image by computer processing of overlapping diffraction patterns (scans). When moving the object it is assumed that the illuminating beam and the position of the detector remain unchanged. Ptychography is used in a wide range of radiation wavelengths from infrared to X-ray, and it is possible to do without imaging optics. In this work, the possibility of obtaining an amplitude-phase image of the surface relief of an object inclined to the incident one was studied.

We consider the 3D coefficient inverse problem for parabolic wave equation. It involves determining the spatial distribution of refractive and absorption indices by processing phase diffraction patterns obtained by irradiating an object with a set of Gaussian beams. Unlike tomography and ptychography, rotation or scanning of the sample is not required. The problem is solved by expanding the wave field and the complex dielectric constant ε(r) over the full set of Gaussian beam functions. To determine ε(r), we obtain a nonlinear matrix equation. The condition of its solvability allows the selection of sampling frequencies by coordinates in accordance with the practical task.

—The progress in the computer science caused wide acceptance of lensless imaging methods, in particular, the phase reconstruction method. It allows phase and amplitude distribution reconstruction in the object plane by mathematical treatment of the diffraction pattern resulting from a coherent beam passage or reflection from an object. In this case, elements of conventional optical systems, i.e., lenses, focusing mirrors, and others are not used. The classical version of the method implies the detector position in the far-field region with respect to the object, which simplifies calculations. However, this condition is not always feasible; therefore, near-field method versions based on the direct application of the wave propagator were proposed in some studies. In this paper, a new version based on a virtual lens is proposed. Then the complexity and computation time remain at the same level as for the far zone, but it is possible to significantly reduce the distance to the detector. The effectiveness of the method is demonstrated in an experiment with a helium-neon laser.

E.G. Bessonov suggested the time integrated strength of an electric field ∫−∞∞E(r,t)dt=SE(r) as a parameter to classify electromagnetic (EM) waves. Since then, this parameter has been studied and used in many works on microwave and laser physics, especially when it comes to unipolar, bipolar and few cycle EM pulses. In this paper, it is shown that SE(r)=0 is an identity for a wide class of free space pulses of finite total energy. This property can be useful in various applications of few cycle radiation and as a benchmark in EM and QED computations.

Ptychography is a lensless imaging technology that is validated from hard X-rays to terahertz spectral range. It is most attractive for extreme ultraviolet (EUV) and X-rays as optical elements are expensive and often not available. Typically, the set up involves coherently illuminated object that directs the scattered radiation normally to detector which is parallel to the object plane. Computer processing of diffraction patterns obtained when scanning the object gives the image, more precisely, the distribution of intensity and phase on its surface. However, this scheme is inefficient for EUV and X-rays due to poor reflectivity and low penetration in all materials. Reflection mode ptychography solves the problem if illumination angles do not exceed the critical angle of object material. Changing the geometry of experiment changes physical and mathematical model of image formation. Including: diffraction integral describing beam propagation from object to detector, inverse problem, optimization of object illumination angle, position and orientation of detector, choosing size and grid of coordinate and frequency computer domains. This paper considers the wavefield scattered to detector by obliquely illuminated object and determines a domain for processing of obtained scans. Solution of inverse problem with phase retrieval and resulting numerical images will be presented in the next paper.

Current approach to space-time coupling (STC) phenomena is given together with a complementary version of the STC concept that emphasizes the finiteness of the energy of the considered pulses. Manifestations of STC are discussed in the framework of the simplest exact localized solution of Maxwell's equations, exhibiting a "collapsing shell". It falls onto the center, continuously deforming, and then, having reached maximum compression, expands back without losing energy. Analytical solutions describing this process enable to fully characterize the field in space-time. It allowed to express energy density in the center of collapse in the terms of total pulse energy, frequency and spectral width in the far zone. The change of the pulse shape while travelling from one point to another is important for coherent control of quantum systems. We considered the excitation of a two-level system located in the center of the collapsing EM (electromagnetic) pulse. The result is again expressed through the parameters of the incident pulse. This study showed that as it propagates, a unipolar pulse can turn into a bipolar one, and in the case of measuring the excitation efficiency, we can judge which of these two pulses we are dealing with. The obtained results have no limitation on the number of cycles in a pulse. Our work confirms the productivity of using exact solutions of EM wave equations for describing the phenomena associated with STC effects. This is facilitated by rapid progress in the search for new types of such solutions.

We analytically study the problem of pore detection and certification in bulk objects by means of radiography. For an absorbent sample, the optimum thickness for pore imaging and detection is expressed in terms of the linear attenuation coefficient of the material. This can be used to maximize the signal-to-noise ratio by tuning the photon energy of the incident monochromatic beam. The problem is more complicated for transparent objects. An evident approach is radiography in coherent beams; in this case, we use a simple model allowing to find the field structure of the transmitted beam on the backside of the sample and beyond in the outer half space in terms of few dimensionless parameters, including the Fresnel number F = a 2 / λz , where a is the pore radius, λ is the wavelength, z is the distance from the back side of the sample to the detector, and the phase number Φ = akδ , with k = 2 π / λ and δ being the bulk material decrement. The detailed analysis of this field structure is performed that can be used to find the optimum position of a detector revealing the pores parameters from the intensity distribution measured. We present the numerical results for a Gaussian type of the pore shape function and provide the software to calculate the space field structure for other pore shape functions. The stationary phase method in higher orders, used here to simplify the Fresnel integral, can be applied to extend the obtained results to 3D geometry. The suggested qualitative picture of the formation of images of pores as phase objects complements modern methods of monitoring porous-sensitive materials.

Ptychography currently seems the most natural and effective method of approaching the diffraction limit of optical resolution. Schematic diagram of a ptychography microscope does not contain refractive or focusing elements. It includes a source of coherent illumination, a platform for (macroscopic) movement of the object, and a detector for recording transmitted or reflected radiation from the object. The detector is connected to a computer that processes diffraction patterns. In this paper, after a brief introduction to the history and current state of ptychography, we consider in detail the wave packet method for calculating the wave field at a detector in the far zone. It allows to establish the relationship between the fields on the object and the detector up to a numerical aperture of ~1. Theoretically substantiated formulas are proposed that determine the size and discretization step of a domain on an object, for given sizes of detector, pixel and object to detector distance. Based on these formulas, a comparison with the paraxial approximation for a point source is performed, as well as modeling of ptychography imaging by the PIE algorithm.

We propose an optical configuration of a reflective mode X-ray microscope which operates by the reflection of radiation incident on an object at grazing incidence. Primary emphasis is placed on the image recording with minimal aberrations. Numerical simulations are used to estimate the spatial resolution and the field of view, and a comparison is made with the results of investigation of surface-modified objects with a reflective mode X-ray laser microscope operating at a wavelength of 14.9 nm.

It is shown that the replacement of X-ray tubes used in coronary angiography with laser-electron X-ray generators improves the quality of imaging and (or) reduces the radiation load on the patient and the expenditure of the contrast agent. The main stages of the angiography procedure are implied to stay unchanged, and the advantages will be achieved at the expense of tuning the radiation spectrum to the absorption maximum of the contrast agent. The parameters of electron bunches and laser pulses interacting with them are determined that, on the one hand, provide the required flux of X-ray radiation and, on the other hand, obey the limitations imposed by the thermal and photoemission properties of the photocathode. These parameters can be implemented using the up-to-date achievements in laser and accelerator technology.

Thomson X-ray source occupying the niche between X-ray tubes and accelerator based facilities has physical properties, size and cost suitable for various applications. One of them - coronary angiography - allows two approaches: (a) replacement of an electron storage ring by Thomson X-ray source in intravenous coronary angiography which is a minimally invasive technique without catheterization, and (b) more recent approach - replacement of X-ray tube in conventional interventional coronary angiography by Thomson X-ray source. Both approaches are reviewed here with the emphasis on (b).

The paper deals with the analysis of absorption contrast of histological and cytological images, which can be produced in soft x-ray/EUV microscopic studies using monochromatic or quazi-monochromatic radiation at the wavelengths 2-14 nm. We present also the experimental results obtained with a laser-plasma source and X-ray multilayer optics in the spectral region of high transparency of carbon-containing materials (4.5-5 nm, "carbon window").

It is well known that contrast high-resolution images are usually produced with normal incidence optics and samples observed normally to their surface. However, a number of recent X-ray experiments from 0.1 to 10 keV demonstrate a quest for imaging of slanted objects and the objects illuminated at grazing angles. A brief survey of previous studies, theoretical consideration, simulation, and application prospects of this new imaging technology is presented.

A new type of a high-brilliance X-ray source known as the Thomson X-ray laser-electron generator (TXG) opens new possibilities for materials characterization by X-ray diffraction methods such as high resolution X-ray diffractometry and topography and diffraction analysis at extreme conditions in shear diamond anvil cells. The advantages of the TXG compared to X-ray laboratory sources are a high flux, a quasi-monochromatic, nearly parallel beam and a tunable wavelength. The paper presents examples of applications as well as estimations of typical photon flux and exposure time saving advantages resulted from an implementation of TXG radiation in a home laboratory.

It was medical applications that stimulated F. Carrol in the early 1990s to start the research of on relativistic Thomson scattering X-ray sources, as a part of the infrastructure of the future society. The possibility to use such a source in interventional cardiology is discussed in this paper. The replacement of X-ray tube by relativistic Thomson scattering Xray source is predicted to lower the patient radiation dose by a factor of 3 while image quality remains the same. The required general characteristics of accelerator and laser units are found. They can be reached by existing technology. A semiempirical method for simulation of medical and technical parameters of interventional coronary angiography systems is suggested.

In this concept study a laser-electron X-ray generator (LEX) is considered for the medical imaging of the inner vessel structure. It is demonstrated that the modern lasers and linear electron accelerators are suitable for the design of the new generation of angiography medical equipment combining higher spatial and time resolution with the reduced patient dose. Angiography setup based on LEXG can make use of different contrast media (iodine, gadolinium) working on absorption edge due to the narrow tuneable spectrum which is not possible with conventional X-ray tubes. In the present study all estimations are made for iodine-based contrast agents. The conclusion is that modern technologies allow practical implementation of LEX for angiography based on multibunch linear accelerator and photon storage device.