scholarly journals Study of thin, achromatic diffractive structures to focus terahertz radiation on a detector

2020 ◽  
Vol 50 (3) ◽  
Author(s):  
Karolina Liebert ◽  
Martyna Rachon ◽  
Andrzej Kolodziejczyk ◽  
Maciej Sypek ◽  
Izabela Ducin ◽  
...  
Keyword(s):  
Optical Axis ◽  
Chromatic Aberration ◽  
Second Order ◽  
Thz Radiation ◽  
Spherical Lens ◽  
Optical Elements ◽  
Point Spread Functions ◽  
Practical Applications ◽  
Energy Maps ◽  
Diffractive Structures

Thin and lightweight achromatic focusing elements with F-number close to 1 are desirable in many practical applications. We present the idea to use diffractive structures designed to work for the substantially increased THz frequency range. The paper analyses mono- and multi-focal lenses forming point-like foci as well as axicon and light sword optical elements focusing THz radiation into line segments located along the optical axis. We consider diffractive elements in a form of the first and the second order kinoforms having various thicknesses. Designed and fabricated elements were numerically and experimentally examined to verify their achromatic functioning. We present point spread functions (XY scans) and 2D energy maps (XZ scans) for different THz frequencies. Moreover, a diagram of chromatic aberration is created by registering energy distribution along the optical axis for different frequencies. The distance corresponding to the highest energy is chosen for each frequency. Therefore, we can compare broadband working of designed structures. The spherical lens coded as kinoform of the second order provides the best broadband functioning, however it is two times thicker than structures providing extended depth of focus (light sword and axicon) working with slightly smaller efficiency but being much thinner.

The imaging properties of electron beams in arbitrary static electromagnetic fields

1952 ◽  
Vol 245 (894) ◽  
pp. 155-187 ◽  
Keyword(s):  
Variational Equation ◽  
Chromatic Aberration ◽  
Relativistic Correction ◽  
Zero Order ◽  
Second Order ◽  
Optical Systems ◽  
Characteristic Functions ◽  
Tensor Calculus ◽  
Paraxial Ray ◽  
Imaging Properties

Electron-optical systems with curved axes—such as mass spectrographs and certain beta-ray spectrometers—have long been in practical use, but there has been available no complete theory of the aberrations of such systems. It is the object of the present paper to construct such a theory and to demonstrate, by an example, its application to practical problems. An appropriate co-ordinate system is set up by means of a ray-axis together with its normal and binormal. The electric and magnetic fields are then investigated with the help of tensor calculus; the variational principle of electron optics is also put into tensor form. The integrand of the variational equation may be separated into a series of polynomials, one of which determines the paraxial imaging properties of the system and the rest of which determine the aberrations. The condition is established for which, upon an appropriate transformation, either of the paraxial ray equations contains only one off-axis co-ordinate. Subsequent investigations are restricted to systems, which are termed ‘orthogonal’, for which this condition is satisfied. It is shown that, in a certain sense, no orthogonal electron-optical system can be wholly divergent. The second-order aberration and the zero-order and paraxial chromatic aberrations are then investigated by the method of perturbation characteristic functions. All formulae are given in their relativistic forms but their non-relativistic forms are indicated; formulae are therefore given for the calculation of the zero-order and paraxial relativistic correction. It is indicated to what extent one forfeits control over the second-order aberration—and hence over the paraxial chromatic aberration also—by specifying that the paraxial behaviour of rays should be Gaussian. As an example, the imaging properties of a helical beam moving in the field of a pair of coaxial cylindrical electrodes are calculated. There is also an appendix which gives formulae for the effect upon aberrations of a change in the aperture position.

scholarly journals DIFFERENTIATION OF POLYNOMIALS IN SEVERAL VARIABLES OVER GALOIS FIELDS OF FUZZY CARDINALITY AND APPLICATIONS TO REED-MULLER CODES

2018 ◽  
Vol 18 (3) ◽  
pp. 339-348
Author(s):  
V. M. Deundyak ◽  
N. S. Mogilevskaya
Keyword(s):  
Coding Theory ◽  
Communication Systems ◽  
Communication Channels ◽  
Galois Field ◽  
Second Order ◽  
Galois Fields ◽  
Practical Applications ◽  
Several Variables ◽  
Confidential Data ◽  
Partial Distortion

Introduction. Polynomials in several variables over Galois fields provide the basis for the Reed-Muller coding theory, and are also used  in a number of cryptographic problems. The properties of such polynomials specified over the derived Galois fields of fuzzy cardinality are studied. For the results obtained,  two  real-world  applications  are  proposed: partitioning scheme and Reed-Muller code decoder.Materials and Methods. Using linear algebra, theory of Galois fields, and general theory of polynomials in several variables, we have obtained results related to the differentiation and integration  of polynomials  in  several  variables  over  Galois fields of fuzzy cardinality. An analog of the differentiation operator is constructed and studied for vectors.Research Results. On the basis of the obtained results on the differentiation and integration of polynomials, a new decoder for Reed-Muller codes of the second order is given, and a scheme for organizing the partitioned transfer of confidential data is proposed. This is a communication system in which the source data on the sender is divided into several parts and, independently of one  another,  transmitted  through  different communication channels, and then, on the receiver, the initial data is restored of the parts retrieved. The proposed scheme feature is that it enables to protect data, both from the nonlegitimate access, and from unintentional errors; herewith, one  and  the  same  mathematical  apparatus  is  used  in  both cases. The developed decoder for the second-order Reed-Muller codes prescribed over the derived odd Galois field may have a constraint to the recoverable error level; however, its use is advisable for a number of the communication channels.Discussion    and    Conclusions.    The    proposed    practical applications   of   the   results   obtained   are   useful   for   the organization of reliable communication systems. In future, it is planned  to  study  the  restoration  process  of  the  original polynomial by its derivatives, in case of their partial distortion, and the development of appropriate applications.

Biquadratic Digital Phase-Compensator Design with Stability-Margin Controllability

2019 ◽  
Vol 28 (04) ◽  
pp. 1950068 ◽  
Author(s):  
Tian-Bo Deng
Keyword(s):  
Stability Margin ◽  
Transformation Method ◽  
Second Order ◽  
Approximation Accuracy ◽  
Parameter Transformation ◽  
Practical Applications ◽  
Compensator Design ◽  
Novel Method ◽  
Design Idea ◽  
The Stability

This paper proposes a novel method for the design of a recursive second-order (biquadratic) all-pass phase compensator with controllable stability margin. The design idea stems from the generalized stability triangle (GST) derived by the author for the second-order biquadratic digital filter. Based on the GST, a parameter-transformation method is proposed on the transformations of the denominator coefficients of the transfer function of the biquadratic phase compensator. The transformations convert the original denominator coefficients to other new parameters, and any values of those new parameters can guarantee that the GST condition is always satisfied. Optimizing the new parameters yields a biquadratic phase compensator that definitely meets a prespecified stability margin. That is, a biquadratic all-pass phase compensator can be designed to have an arbitrarily specified stability margin. This in turn avoids the occurrence that a recursive phase compensator may become unstable in the practical applications. Thus, the resulting biquadratic phase compensator has robust stability, which is extremely important during the practical filtering operations. A design example is given to show the stability margin guarantee as well as the approximation accuracy.

NEW GENERATION OPTICAL ELEMENTS WITH CENTRALLY SYMMETRIC ORIENTATION BASED ON LIQUID CRYSTAL POLYMERS

2020 ◽  
Vol 54 (1 (251)) ◽  
pp. 70-76
Author(s):  
H.L. Margaryan ◽  
N.H. Hakobyan ◽  
V.K. Abrahamyan ◽  
V.V. Belyaev ◽  
D.N. Chausov ◽  
...  
Keyword(s):  
Liquid Crystal ◽  
Optical Axis ◽  
Periodic Structures ◽  
Liquid Crystal Polymers ◽  
Optical Elements ◽  
Smooth Change ◽  
Ultrathin Layers ◽  
Centrally Symmetric ◽  
New Type ◽  
New Generation

The synthesis of new photo-orienting liquid crystal polymers made it possible to create a completely new type of optical elements consisting of ultrathin layers with a spatially structured orientation of the optical axis. In this paper the optical elements based on centrally symmetric periodic structures with cylindrical orientations of molecules are described. These elements are implemented using the recording method that provides a smooth change of optical axis in a thin film of a liquid crystal polymer. The optical elements on the base of described structures have new functionalities and may be assigned to the class of optical elements of a new generation.

High-performance EUV/soft X-ray ellipsometry system using multilayer mirrors

1998 ◽  
Vol 5 (3) ◽  
pp. 735-737 ◽  
Author(s):  
Tomoaki Kawamura ◽  
Jean-Jacques Delaunay ◽  
Hisataka Takenaka, ◽  
Takayoshi Hayashi ◽  
Yoshio Watanabe
Keyword(s):  
High Performance ◽  
Extinction Ratio ◽  
Second Order ◽  
Multilayer Mirrors ◽  
Optical Elements ◽  
X Ray ◽  
First Order

A high-performance EUV/soft X-ray ellipsometry system using multilayer mirrors has been developed. A couple of multilayer mirrors were used for the polarizer, and two multilayer mirrors were used for the rotating analyser. The multilayer mirrors were optimized to obtain a medium extinction of about 2000. An extinction ratio of the polarizer up to 104 can be achieved by using two multilayer mirrors, and the calculated reflectivity was more than 35%. The calculated error of the optical elements reveals that the error of the polarizer and misalignment optical parts is mainly of the first order, and that of the analyser is of the second order.

scholarly journals CALCULATION OF THE ACHROMATIC DIFFRACTION SYSTEM WITH CORRECTED SPHERICAL ABERRATION (part 2)

2020 ◽  
Vol 8 (1) ◽  
pp. 127-133
Author(s):  
Yury Ts. Batomunkuev ◽  
Alexandra A. Pechenkina
Keyword(s):  
Spherical Aberration ◽  
Focal Length ◽  
Optical Element ◽  
Diffraction Order ◽  
Image Plane ◽  
Chromatic Aberration ◽  
Real Image ◽  
Optical Elements ◽  
A Value ◽  
Analytical Expressions

Achromatization of a three-component diffraction system consisting of one thick and two thin hologram optical elements is considered in the work. Analytical expressions are obtained for correcting the chromatic aberration of the position of a thick focusing hologram optical element by two scattering thin hologram optical elements in a given spectrum range. It is shown that achromatization is achieved for such a three-component system using two thin hologram elements located symmetrically on both sides of the thick element and having a value of the working diffraction order greater than the ratio of the focal length to the distance from the thin element to the image plane (at a given wavelength). The proposed three-component holographic system can be used to convert both an imaginary image into a real image and a real into an imaginary image in predetermined spectral regions of the visible, ultraviolet or infrared ranges of the spectrum.

scholarly journals All Femtosecond Optical Pump and X-Ray Probe: Holey-Axicon for Free Electron Laser

2020 ◽  
Author(s):  
Vijayakumar Anand ◽  
Jovan Maksimovic ◽  
Tomas Katkus ◽  
Soon Hock Ng ◽  
Orestas Ulcinas ◽  
...  
Keyword(s):  
Free Electron ◽  
Free Electron Laser ◽  
Optical Axis ◽  
Bessel Beam ◽  
X Rays ◽  
Temporal Dimension ◽  
Optical Elements ◽  
Optical Pump ◽  
X Ray ◽  
Fs Laser

We put forward a co-axial pump(optical)-probe(X-rays) experimental concept and show performance of the optical component. A Bessel beam generator with a central 100 micrometers-diameter hole (on the optical axis) was fabricated using femtosecond (fs) laser structuring inside a silica plate. This flat-axicon optical element produces a needle-like axial intensity distribution which can be used for the optical pump pulse. The fs-X-ray free electron laser (X-FEL) beam of sub-1 micrometer diameter can be introduced through the central hole along the optical axis onto a target as a probe. Different realisations of optical pump are discussed. Such optical elements facilitate alignment of ultra-short fs-pulses in space and time and can be used in light-matter interaction experiments at extreme energy densities on the surface and in the volume of targets. Full advantage of ultra-short 10 fs X-FEL probe pulses with fs-pump(optical) opens an unexplored temporal dimension of phase transitions and the fastest laser-induced rates of material heating and quenching. A wider field of applications of fs-laser-enabled structuring of materials and design of specific optical elements for astrophotonics is presented.

scholarly journals Liquid Crystal Spatial Light Modulator with Optimized Phase Modulation Ranges to Display Multiorder Diffractive Elements

2019 ◽  
Vol 9 (13) ◽  
pp. 2592 ◽  
Author(s):  
Elisabet Pérez-Cabré ◽  
María Sagrario Millán
Keyword(s):  
Liquid Crystal ◽  
Phase Modulation ◽  
Spatial Light Modulator ◽  
Visible Spectrum ◽  
Chromatic Aberration ◽  
Light Modulator ◽  
Optical Elements ◽  
First Order ◽  
Large Phase ◽  
Liquid Crystal On Silicon

A liquid crystal on silicon spatial light modulator (LCoS SLM) with large phase modulation has been thoroughly characterized to operate optimally with several linear phase modulation ranges (π, 2π, 3π, 4π, 6π, and 8π) for an intermediate wavelength of the visible spectrum (λG = 530 nm). For each range, the device response was also measured for two additional wavelengths at the blue and red extremes of the visible spectrum (λB = 476 nm and λR = 647 nm). Multiorder diffractive optical elements, displayed on the LCoS SLM with the appropriate phase modulation range, allowed us to deal with some widely known encoding issues of conventional first-order diffractive lenses such as undersampling and longitudinal chromatic aberration. We designed an achromatic multiorder lens and implemented it experimentally on the SLM. As a result, the residual chromatic aberration reduces to one-third that of the chromatic aberration of a conventional first-order diffractive lens.

Analysis of Flexibility and Stability of Crane Telescopic Boom with Elastic Restraint and Second-Order Effect

2013 ◽  
Vol 774-776 ◽  
pp. 109-113
Author(s):  
Liang Du ◽  
Nian Li Lu ◽  
Peng Lan
Keyword(s):  
Stability Analysis ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Order Effect ◽  
Second Order ◽  
Analysis Model ◽  
Characteristic Equations ◽  
Lateral Deflection ◽  
Practical Applications ◽  
Vertical Stability

The cylinder support crane telescopic booms deformation and stability analysis model in the lifting plane is equivalent with the multistep column with elastic restraint. To analyze the lateral flexibility and vertical stability of the telescopic booms with elastic restraint accurately, this paper established the deflection differential equations of multi-sectioned telescopic booms with second-order effect, introduced proper boundary conditions, obtained the precise recurrence lateral deflection differential equations and the buckling characteristic equations of arbitrary sectioned telescopic booms, and some practical applications of the buckling characteristic equations were presented. Took certain five-sectioned telescopic booms as example, by comparing the results with ANSYS method, the accuracy of the equations deduced in this paper was verified.

Parasitic Flux Analysis of Cooled Infrared Detectors for Space Applications

2017 ◽  
Vol 67 (2) ◽  
pp. 193
Author(s):  
Ankur Jain ◽  
Amiya Biswas
Keyword(s):  
Infrared Detector ◽  
Optical Design ◽  
Spectral Band ◽  
Low Noise ◽  
Flux Analysis ◽  
Optical Elements ◽  
Space Applications ◽  
Practical Applications ◽  
Spectral Bands ◽  
Infrared Imager

An infrared imager measures radiations emitted by an object in specified spectral bands to determine change in object’s characteristics over a period of time. A typical infrared imager consists of focusing optics and a cryogenically cooled two-dimensional infrared detector array mounted on the cold tip of an active micro-cooler vacuum sealed with an optical window, typically known as integrated detector cooler assembly (IDCA). Detection of feeble radiant flux from the intended target in a narrow spectral band requires a highly sensitive low noise sensor array with high well capacity. However, in practical applications the performance of an infrared imager is limited by the parasitic thermal emissions from optical elements and emissions from IDCA components like vacuum window, Dewar walls which are generally kept at ambient temperature. To optimise the performance of imager it becomes imperative to estimate these parasitic fluxes and take corrective actions to minimise their effects. This paper explains an analytical model developed to estimate parasitic fluxes generated from different components of a long wave infrared imager. Validation of the developed model was carried out by simulations in ZEMAX optical design software using ray trace method after analytical computations in MATLAB.

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