Heterodyne Meter of Transverse and Longitudinal Displacements of Objects
Arkady Arsenyevich Titov,
Mikhail Mikhailovich Bakharev
Issue:
Volume 6, Issue 3, September 2021
Pages:
41-46
Received:
2 June 2021
Accepted:
16 June 2021
Published:
28 July 2021
Abstract: Nowadays, optical methods are widely used to measure the movements of various objects. In this case, it is necessary to measure both longitudinal displacements at a large distance, and transverse ones. Such tasks have to be solved when measuring the displacements of the cutting tools of machine tools. Among the optical methods, the most accurate is the method of heterodyne interferometry. However, this method does not allow making absolute measurements, since the period of the interference pattern is commensurate with the wavelength of light, which requires counting the number of stripes. In addition, the readjustment of this method requires two-frequency lasers and rather complex optical and electronic systems, which significantly complicates their application. To solve this problem, we used the method of heterodyne interferometry developed by the authors, which, in contrast to the known methods, allows us to make absolute measurements of the parameters of objects. This is achieved by creating a period of the interference pattern, which is equal to the speed of sound in the acousto-optical modulator divided by the modulator control frequency. The result was aa block diagram of a device for measuring transverse and longitudinal displacements of objects by the heterodyne method is developed. Analytical expressions are obtained for calculating the signal strength at the photodetector, the periods of interference patterns, the phase shift depending on the transverse and longitudinal displacements, the measurement range and the measurement accuracy, which allowed us to determine the main parameters of the device. To confirm the results obtained, an experiment was carried out. For this, a block diagram of the experiment was developed, with the help of which the influence of the beam divergence on the period of the interference pattern was determined. The experiment showed good agreement between theory and experiment.
Abstract: Nowadays, optical methods are widely used to measure the movements of various objects. In this case, it is necessary to measure both longitudinal displacements at a large distance, and transverse ones. Such tasks have to be solved when measuring the displacements of the cutting tools of machine tools. Among the optical methods, the most accurate is...
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Taylor Series and Getting the General Solutions for the Equations of Motion Using Poisson Bracket Relations
Issue:
Volume 6, Issue 3, September 2021
Pages:
47-51
Received:
26 June 2021
Accepted:
28 July 2021
Published:
4 August 2021
Abstract: In mathematics and classical mechanics, the Poisson bracket is an important binary operation in Hamiltonian mechanics, playing a central role in Hamilton's equations of motion, which govern the time evolution of a Hamiltonian dynamical system. The Poisson bracket also distinguishes a certain class of coordinate transformations, called canonical transformations, which map canonical coordinate systems into canonical coordinate systems. In this work we study some examples from the classical mechanics of particles and apply mathematical method for building the equation of motion. In the present paper Poisson Brackets and their properties are presented, by using Poisson brackets and their properties we calculate some brackets. We use the Poisson bracket with Hamiltonians to express the time dependence of a function u (t), the main idea Taylor series is taken as the required solution for equation of motion using the properties of the Poisson Brackets, We have examined examples from the classical mechanics to illustrate the idea such as motion with a constant acceleration, simple harmonic oscillator, freely falling particle. The solutions are compatible with what is known in classical mechanics. The work is fundamental and sheds new light onto classical mechanics. Poisson brackets are a powerful and sophisticated tool in the Hamiltonian formalism of Classical Mechanics. They also happen to provide a direct link between classical and quantum mechanics.
Abstract: In mathematics and classical mechanics, the Poisson bracket is an important binary operation in Hamiltonian mechanics, playing a central role in Hamilton's equations of motion, which govern the time evolution of a Hamiltonian dynamical system. The Poisson bracket also distinguishes a certain class of coordinate transformations, called canonical tra...
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Terahertz TWT on a Rectangular Waveguide Folded in a Circular Spiral
Alexander Kurayev,
Vladimir Matveyenka
Issue:
Volume 6, Issue 3, September 2021
Pages:
52-54
Received:
26 June 2021
Accepted:
24 July 2021
Published:
27 September 2021
Abstract: The most promising in the THz range is traveling-wave tubes (TWTs) and backward-wave tubes (BWTs) on a serpentine-curved (zigzag-rolled) rectangular waveguide. They are implemented in the THz range (220 GHz), although their characteristics are far from satisfactory due to the strict restriction on the tape electron beam width, that does not allow reaching the summarizing beam current optimum level. To replace the zigzag convoluted waveguide with the spiraled for the TWT and BWT on a curved rectangular waveguide is the best way to remove the ribbon beam width restriction. In the early TWT and BWT design a waveguide planar spiral was also flat in the upper and lower parts connected by vertical idle (without beam) transitions. Proposed design can be significantly improved both in relation to the electron interaction process with the waveguide field and in relation to the TWT-BWT manufacturing technology if instead of a planar waveguide spiral, a circular one is used. The article proposes the TWT designing a terahertz rectangular waveguide folded as a circular spiral. The design differs from the previously proposed TWT with a planar-spiral waveguide by the improved interaction conditions between the electron beam and the waveguide field, as well as the manufacturing technology simplification for terahertz range. Based on numerical simulation, it is shown that proposed TWT achieves Gн= 42 ÷ 48dB saturation gain in the 220 GHz range with the waveguide turn number n = 40 ÷ 50. The proposed TWT design on a rectangular waveguide folded in a circular spiral is more technologically advanced than the TWT on a planar-spiral waveguide. In the most necessary 220 GHz range the efficiency is very high and can provide the need for amplifiers and generators in this and other ranges. We also note that the TWT on a spirally folded waveguide can operate in the BWT mode and, moreover, simultaneously in the TWT and BWT modes. The latter is possible in modes close to linear one. The TWT magnetic system of the type described above can be implemented in the form of a permanent magnet with pluses on the TWT end parts. The proposed TWT characteristics can be significantly improved by optimizing the waveguide helical winding pitch. Exactly as it is achieved with using the spiral wire deceleration system. The efficiency of such optimized TWT reaches 70% efficiency.
Abstract: The most promising in the THz range is traveling-wave tubes (TWTs) and backward-wave tubes (BWTs) on a serpentine-curved (zigzag-rolled) rectangular waveguide. They are implemented in the THz range (220 GHz), although their characteristics are far from satisfactory due to the strict restriction on the tape electron beam width, that does not allow r...
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