arXiv subjects

V. Yu. Terebizh

Publications and source records attributed to V. Yu. Terebizh.

15 recordsLinked to original sources

arXiv2025

Simple model of violent relaxation of a spherical stellar system

A spherical system with arbitrary mean velocities in the radial and transverse directions, but with zero dispersion of radial velocities, is considered as a model describing the violent relaxation of star clusters and galaxies. The model allows to reduce the infinite chain of Jeans' equations of moments to just three hydrodynamic equations. The found system of equations is consistent with the law of conservation of energy and the virial equation. This part of the work is devoted to a general description of the model, then the calculation results will be presented.

astro-ph.GA↗

arXiv2023

On the evolution of a stellar system in the context of the virial equation

The virial equation is used to clarify the nature of the dynamic evolution of a stellar system. Compared to the kinetic equation, it gives a deeper but incomplete description of the process of relaxation to a quasi-stationary state, which here means the fulfillment of the virial theorem. Analysis shows that the time to reach the virial equlibrium state $T_v$ is about two to three dozen dynamic time periods $T_d$. Namely, during $T_v$ the virial ratio, the mean harmonic radius, and the root-mean-square radius of the system fluctuate, and then the first two characteristics stabilize near their equilibrium values, while the root-mean-square radius continues to grow (possibly ad infinitum). This indicates a fundamentally different behavior of the moment of inertia of the system relative to the center of gravity and its potential energy, leading to the formation of a relatively small equilibrium core and an extended halo.

astro-ph.GA↗

arXiv2022

Two-mirror aplanatic telescopes with a flat field

A complete description is given of two-mirror telescopes with a flat medial focal surface, on which the images of stars are circles of least confusion. Particular attention is paid to aplanats, since their field of view is noticeably larger than that of classical systems. Two sets of appropriate solutions correspond to Schwarzschild and Gregorian telescopes. As a result, it becomes possible to use flat light detectors with wide-field two-mirror telescopes. New designs are of particular interest when as few reflective surfaces as possible are required, which is typical for space exploration and non-optical observations.

astro-ph.IM↗

arXiv2017

Space telescope designed for accurate measurements

A modified version of the folded aplanatic Gregory telescope equipped with a spherical two-lens corrector is proposed for observations requiring a high signal-to-noise ratio. The basic telescope model has an aperture of 400 mm (f/3.0), its field of view is 3.0 degrees, the linear obscuration is 0.12, the distortion is less than 0.5%. The focal surface has a spherical shape; the achieving of a plane field requires an increase in the number of lenses in the corrector. The images of stars in the integrated wavelength range 0.35 - 1.0 mcm are close to the diffraction-limited ones (D_{80} = 5.9 - 8.2 mcm = 1.0 - 1.4 arc seconds). The system is free from direct background illumination; both the lens corrector and the light detector are protected from cosmic particles.

astro-ph.IM↗

arXiv2017

Statistical approach to linear inverse problems

The main features of the statistical approach to inverse problems are described on the example of a linear model with additive noise. The approach does not use any Bayesian hypothesis regarding an unknown object; instead, the standard statistical requirements for the procedure for finding a desired object estimate are presented. In this way, it is possible to obtain stable and efficient inverse solutions in the framework of classical statistical theory. The exact representation is given for the feasible region of inverse solutions, i.e., the set of inverse estimates that are in agreement, in the statistical sense, with the data and available a priory information. The typical feasible region has the form of an extremely elongated hole ellipsoid, the orientation and shape of which are determined by the Fisher information matrix. It is the spectrum of the Fisher matrix that provides an exhaustive description of the stability of the inverse problem under consideration. The method of constructing a nonlinear filter close to the optimal Kolmogorov-Wiener filter is presented.

stat.ME↗

arXiv2016

On the capabilities of survey telescopes of moderate size

To explore capabilities of moderate-size optical telescopes in surveys, the set of 9 new wide-field designs having apertures up to 1 m is considered. All but one systems have angular field of view in a range 3.5-10 degrees and flat focal surface; the field of the last system is 45 degrees in diameter at the 0.5 m aperture and spherical focal surface. The complete description of the optical layouts is given in the Appendix. Relations between the expected limiting magnitude, survey speed and exposure time allow to choose the system that is most suitable for a particular task of observations. In principle, a single wide-field telescope with the aperture of approximately 1 m can detect objects brighter than 22.5 magnitude over the entire hemisphere within one night, however, the reliability of acquired data can be significantly increased by using a hierarchic observational network comprised of telescopes with optimized parameters.

astro-ph.IM↗

arXiv2016

All-spherical telescope with extremely wide field of view

An all-spherical catadioptic telescope with the angular field of view of several tens of degrees in diameter and spherical focal surface is proposed for the monitoring of large sky areas. We provide a few examples of such a system with the apertures up to 800 mm and the field of view $30^\circ$ and $40^\circ$ in diameter. The curvature of the focal surface is repaid by high performance of the telescope. In particular, the diameter of a circle, that includes 80% of energy in the polychromatic image of a star, is in the range $1.4'' - 1.9''$ across the field of $30^\circ$ size and $2.2'' - 2.9''$ for the field of $40^\circ$ size. Some ways of working with curved focal surfaces are discussed.

astro-ph.IM↗

arXiv2015

All-spherical telescope with extremely wide field of view

An all-spherical catadioptic system made of glass of one type is proposed for the monitoring of large sky areas. We provide an example of such a system with the aperture of diameter 400 mm and the curved field of 30 degree in diameter.

astro-ph.IM↗

arXiv2014

Autocollimating compensator for controlling aspheric optical surfaces

A compensator (null-corrector) for testing aspheric optical surfaces is proposed, which enables i) independent verification of optical elements and assembling of the compensator itself, and ii) ascertaining the compensator position in a control layout for a specified aspheric surface. The compensator consists of three spherical lenses made of the same glass. In this paper, the scope of the compensator expanded to a surface speed ~f/2.3; a conceptual example for a nominal primary of Hubble Space Telescope is given. The autocollimating design allows significant reducing difficulties associated with practical use of lens compensators.

astro-ph.IM↗

arXiv2007

A purely reflective large wide-field telescope

Two versions of a fast, purely reflective Paul-Baker type telescope are discussed, each with an 8.4-m aperture, 3 deg diameter flat field and f/1.25 focal ratio. The first version is based on a common, even asphere type of surface with zero conic constant. The primary and tertiary mirrors are 6th order aspheres, while the secondary mirror is an 8th order asphere (referred to here for brevity, as the 6/8/6 configuration). The D_80 diameter of a star image varies from 0''.18 on the optical axis up to 0''.27 at the edge of the field (9.3-13.5 mcm). The second version of the telescope is based on a polysag surface type which uses a polynomial expansion in the sag z, r^2 = 2R_0z - (1+b)z^2 + a_3 z^3 + a_4 z^4 + ... + a_N z^N, instead of the common form of an aspheric surface. This approach results in somewhat better images, with D_80 ranging from 0''.16 to 0''.23, using a lower-order 3/4/3 combination of powers for the mirror surfaces. An additional example with 3.5-m aperture, 3.5 deg diameter flat field, and f/1.25 focal ratio featuring near-diffraction-limited image quality is also presented.

astro-ph↗

arXiv2007

Wide-field telescopes with a Mangin mirror

Two all-spherical catadioptric optical systems with a Mangin mirror are described. The design A (aperture 500 mm, f/2.0) has flat field of view of 7 deg in diameter; the design B (aperture 1000 mm, f/1.7) has 10-deg flat field. Both designs show near-diffraction-limited images. The D_80 diameter for the design A in the integral waveband 0.45-0.85 mcm varies from 1''.3 on the optical axis up to 2''.2 at the edge of the field (6.2-10.7 mcm); the corresponding range of the D_80 diameter for the design B is 1''.5-1''.9 (12.4-16.2 mcm). The designs include simple glass types, mainly Schott N-BK7 and fused silica. In case of need, better images could be attained by a choice of other glass, aspherisation of some surfaces, etc.

astro-ph↗

arXiv2006

Wide-field Corrector for a Gregory Telescope

A form of prime focus corrector for the Gregory system is proposed that provides the sub-arcsecond field of view up to 3 degrees in diameter for the spectral range 0.35-0.90 microns. The corrector includes five lenses made of same glass (fused silica is preferable). The distinctive feature of the corrector consists in dissimilar use of the central and edge zones of a front lens disposed in the exit pupil of a two-mirror system. As an example, the f/1.9 telescope is considered with the 6.5-m aperture and the total length 8.8~m. Its primary and secondary mirrors are pure ellipsoids close to concave paraboloid and concave sphere, respectively. In the basic configuration, all surfaces of the corrector are spherical. The diameter of a star image D_{80} varies from 0''.25 on the optical axis up to 0''.50 at the edge of the 2.3-deg field. Only slightly worse images shows spherical corrector for the 2.4-deg field of view. The fraction of vignetted rays grows on 1.7% from the center of field to its edges. Aspherization of some lens surfaces allows to reach sub-arcsecond images in the field of 3.0 in diameter.

astro-ph↗

arXiv2005

Two-mirror Schwarzschild aplanats. Basic relations

It is shown that the theory of aplanatic two-mirror telescopes developed by Karl Schwarzschild in 1905 leads to the unified description both the prefocal and the postfocal systems. The class of surfaces in the ZEMAX optical program has been properly extended to ascertain the image quality in exact Schwarzschild aplanats. A comparison of Schwarzschild aplanats with approximate Ritchey-Chretien and Gregory-Maksutov aplanatic telescopes reveals a noticeable advantage of the former at fast focal ratio of the system.

astro-ph↗

arXiv2004

Quasi-Optimal Filtering in Inverse Problems

A way of constructing a nonlinear filter close to the optimal Kolmogorov - Wiener filter is proposed within the framework of the statistical approach to inverse problems. Quasi-optimal filtering, which has no Bayesian assumptions, produces stable and efficient solutions by relying solely on the internal resources of the inverse theory. The exact representation is given of the Feasible Region for inverse solutions that follows from the statistical consideration.

math-ph↗

arXiv2004

A Wide-Field Corrector at the Prime Focus of a Ritchey-Chretien Telescope

We propose a form of a lens corrector at the prime focus of a hyperboloidal mirror that provides a flat field of view up to 3 deg diameter at image quality D_{80} < 0.8 arcsec in integrated (0.32-1.10 mcm) light. The corrector consists of five lenses made of fused silica. Only spherical surfaces are used, so the system is capable of achieving better images, if necessary, by aspherizing the surfaces. The optical system of the corrector is stable in the sense that its principal features are retained when optimized after significant perturbations of its parameters. As an example, three versions of the corrector are designed for the V.M.Blanco 4-m telescope at Cerro Tololo Inter-American Observatory with 2.12 deg, 2.4 deg, and 3.0 deg fields of view.

astro-ph↗