RU2575538C1 - Method of obtaining images of space object observed through turbulent atmosphere - Google Patents

Abstract

FIELD: physics.

SUBSTANCE: invention can be used in astronomy and optical location to obtain atmospherically undistorted images of small-size space objects.

EFFECT: high diffraction resolution of the obtained images of small-size space objects and high accuracy of recovering the atmospherically undistorted modulus and phase of the spatial spectrum thereof.

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Description

The invention relates to the field of optical instrumentation and can be used in astronomy and optical location to obtain undistorted atmosphere images of small space objects.

There is a method of obtaining images of a space object observed through a turbulent atmosphere, based on the telescopic formation of a long-exposure image of a space object distorted by the atmosphere and its subsequent spatial filtering to obtain an image undistorted by the atmosphere. This method is described in article R.B. Leighton "Concerning the problem of making sharper photographs of the planets", Sci. Am., V. 194, p. 156, 1956.

The disadvantage of this method is the loss of small image details when averaging atmospheric distortions in the process of recording images for a time longer than the interval of time correlation of atmospheric fluctuations. This method, proposed in astronomy, is used to obtain images of extended spatially invariant regions of outer space.

A known method of obtaining images of a space object observed through a turbulent atmosphere, based on the registration of a hologram with a reference beam passing through the same turbulence as the light from the object, and the subsequent restoration of the undistorted image of the object from the hologram. This method is described in J.D. Gaskill "Imaging through a randomly inhomogeneous medium wavefront reconstruction", J. Opt. Soc. Am., V. 58, p. 600, 1968.

The disadvantage of this method is the need for a reference point source in the isoplanatic region of the isoplanarity, as well as the need for coherent laser illumination of both the observed object and the reference point object, for example, an angular reflector.

A known method of obtaining images of a space object observed through a turbulent atmosphere, based on the registration in a telescope of a series of spectrally-filtered, short-exposure images of an object distorted by a turbulent atmosphere, converting them according to the Fourier into the region of the spatial spectrum, quadratic detection of spatial spectra, averaging them over the series and obtaining the square of the spatial spectrum modulus undistorted by the atmosphere from the object when normalizing the mean square of the the natural spectrum of the image per square module of the optical transfer function of the atmosphere-telescope system.

This method is described in A. Labeyrie's article "Spekle interferometry and possible extensions" Astron and Astrophys, Suppl. Ser., V. 15, p. 464, 1974.

The disadvantage of this method is that when the inverse Fourier transform of the square module of the spatial spectrum of the object is restored only the autocorrelation of the image of the object, and not the image itself. The impossibility of obtaining an image of an object is caused by the loss in processing of the phase of the spatial spectrum, which limits the class of objects observed in this way to only centrally symmetric. In this way, in astronomy, the angular diameters of many stars are determined and binary star structures are allowed.

This drawback of phase loss has been eliminated in the method for acquiring images of a space object observed through a turbulent atmosphere described in K.T. Knox., B.G. Thompson "Recovery of images from atmospherically degraded short exposure photographs" Astron J, v. 193, p L 45, 1974 and taken here as a prototype.

This method is based on the formation by a ground telescope of an atmospheric image of the object, its spectral filtering and quadratic detection for a time shorter than the time correlation interval of atmospheric fluctuations, registration of a series of N such spectrally-filtered, short-exposure images, their Fourier transform to the spatial spectrum and statistical processing the components of the spatial spectra of the recorded images of the series, in which the restoration of the undistorted quad This module of the spatial spectrum from the object is carried out by the A. Labeyrie method (previous analogue), and to reconstruct the phase of the spatial spectrum from the object, double correlations of the spatial spectra of images are formed and the difference phases are restored, “stitching” them from the beginning of the space-frequency region and restoring the phase undistorted by the atmosphere spatial spectrum of the observed space object. Combining further the reconstructed modulus and phase, they form the spatial spectrum, with the inverse Fourier transform, from which the image of the observed space object is undistorted by the atmosphere.

/D, определяемое диаметром приемной апертуры телескопа D. Действительно, преодолев в прототипе ограничения на разрешение, накладываемые турбулентностью атмосферы

/r₀, где r₀ - пространственный радиус корреляции атмосферных флуктуаций (так называемый параметр Фрида), сталкиваемся с проблемой ограниченного углового разрешения апертуры формирующего телескопа. Это ограничение препятствует получению информативных изображений малоразмерных космических объектов.The disadvantage of the prototype is the diffraction limit of the achieved resolution

/ D, determined by the diameter of the receiving aperture of the telescope D. Indeed, overcoming in the prototype resolution restrictions imposed by atmospheric turbulence

/ r₀where r₀ is the spatial radius of the correlation of atmospheric fluctuations (the so-called Fried parameter), we are faced with the problem of limited angular resolution of the aperture of the forming telescope. This limitation prevents the obtaining of informative images of small-sized space objects.

The claimed method for obtaining images of a space object observed through a turbulent atmosphere, in contrast to the known methods and prototype, is based on solving the problem of limited angular resolution of single-aperture optical systems based on aperture synthesis technologies in the formation and recording of images with the subsequent solution to the problem of "vision" through a turbulent atmosphere based on the statistical processing of the modules and phases of the spatial spectra of the recorded images.

The technical result of the claimed invention is to increase the diffraction resolution of the generated images of a small space object and to increase the accuracy of restoration of the module undistorted by the atmosphere and the phase of its spatial spectrum.

The claimed technical result is achieved in that the method of obtaining images of a space object observed through a turbulent atmosphere,

based on the formation of a terrestrial image of a space object by a ground-based optical system,

δ_θ и квадратичном детектировании каждого за время экспонирования

, меньшее

- интервала временной корреляции атмосферных флуктуаций, через промежутки времени

, большие

,their spectral filtering in the band Δλ <Δλ _A =

δ _θ and quadratic detection of each during exposure

less

- interval of time correlation of atmospheric fluctuations, at intervals

large

,

 registration of series of N such atmospheric distortion independent spectrally filtered, short exposure images,

transforming each of them according to Fourier into the region of the spatial spectrum

and the statistical processing of the modules and phases of the spatial spectra of the recorded images of the series for restoring the atmosphere undistorted module and phase of the spatial spectrum of the observed space object,

the formation on them of the spatial spectrum of the object, undistorted by the atmosphere, and obtaining, with the inverse Fourier transform, the image of the observed space object, undistorted by the atmosphere, from it, characterized in

that the formation of atmospheric images of a space object distorted by the atmosphere is carried out by a coherent matrix of M ground-based mobile telescopes of diameter D in the process of space-time aperture synthesis,

in which at first the individual matrix telescopes are arranged in a circle at the center of the matrix, if the object is at the zenith, or along the coherence ellipse, which is the intersection of the aperture synthesis plane with the rotation paraboloid aimed at the oblique observation object,

 then, to obtain a series of independent, spectrally-filtered, short-exposure images of the observed space object, synchronous movement of the matrix’s moving telescopes from its center to the periphery is carried out, preserving their relative position along coherence ellipses,

and to ensure smooth movement and eliminate jolts, continuous movement of the matrix telescopes along rail tracks extending radially from the center of the matrix to its periphery,

while the orientation of each matrix telescope relative to the center of the matrix is maintained unchanged and the combined sub-beams are directed from movable telescopes along rail tracks to the center of the matrix,

where a fixed base station is located, in which both coherent combination of radially propagating sub-beams is performed during the aperture synthesis of the generated images, and quadratic detection of the generated and spectrally filtered images, with their subsequent registration and processing,

while registering a series of N independent, spectrally-filtered, short-exposure images of the observed space object for each k-th relative position of the moving matrix telescopes,

in the statistical processing of the modules and phases of the spatial spectra of a series of recorded images distorted by the atmosphere, use the island nature of the optical transfer function (OPF) of the matrix along the coherence ellipses and its OPF peninsula in the radial direction, extending from the center of the space-frequency region to the cutoff frequency of the synthesized aperture of diameter D _E , and restore the atmosphere-undistorted phase of the spatial spectrum from the object in the islands and peninsulas, deploying it from the center to peripherals

carry out the stitching of the radially reduced phases over the entire spatial frequency region of the aperture synthesis using the triple correlation method with the unfolding of the equations of the closed phases along the coherence ellipses

перед корреляционным усреднением статистической обработки, сглаживают все тройные произведения в пределах островов по всем возможным тройкам замкнутых частот

и,in this case, for small-sized space objects not resolvable by individual matrix telescopes (θ ₀ <

Before correlation averaging of statistical processing, all triple products within the islands are smoothed over all possible triples of closed frequencies

and,

by performing a similar smoothing during statistical processing of the squares of the spatial spectrum moduli of the recorded images, the phase and the spatial spectrum modulus of the object are undistorted by the atmosphere,

combining these, they form the spatial spectrum of the object and, when the Fourier transform is inverse, they receive from it an undistorted image of the observed space object.

The features and essence of the claimed invention are explained in the following detailed description, illustrated by drawings.

In FIG. 1 presents a possible implementation scheme of the proposed method, where:

1 - a flat area in the highlands (diameter 100 m) for placement of the aperture synthesis matrix;

2 - rail tracks for the radial movement of movable matrix telescopes;

3 - shelters for movable matrix telescopes, protecting telescopes from adverse weather conditions;

4 - wind protection of the matrix and its individual elements, reducing wind loads on the telescopes of the matrix in the process of their work outside the shelters;

5 - movable telescopes of a matrix with a diameter of D = 3 ÷ 5 m on a biaxial "alt-alt" mount;

5 * - combinable sub-beams from movable telescopes;

6 - matrix base station.

In FIG. 2 shows the coherence ellipses of the relative position of the moving matrix telescopes during imaging of aperture synthesis, where:

7 - ellipses of coherence;

8 - object of observation;

9 - oblique line of observation;

10 - paraboloid of rotation.

In FIG. 3 presents possible alt-alt mountings of movable matrix telescopes - 5, where:

a) frame;

b) plug.

In FIG. 4 presents a diagram of the construction of the optical-mechanical path (OMT) of the moving element - the matrix of aperture synthesis, where:

11 - telescope of a movable element of a matrix of diameter D;

12 - focus stabilization system - 13;

13 - focus;

14 - dichroic filter with a passband ∆λ = 1000 Å;

15 - television guiding device;

16 - control unit for telescope drives - 11;

17 - recollecting optics;

18 - beam rotation compensator;

19 - dichroic cleavage;

20 - block tracking infrared guide beam from the central station - 6;

21 - control unit for the angular position of the beam;

22 - control unit of the angular position of the beam 5 *;

23 - output of the movable matrix element.

In FIG. 5 is a diagram of the construction of an optical-mechanical path (OMT) of a fixed base station — 6 aperture synthesis matrices, where:

24 - optical input of a fixed element of the matrix;

25 - compensator differences of stroke;

26 - interferometer;

27 - compensator jitter images;

28 - periscope system;

29 - forming telescope;

30 - dichroic filter with a passband ∆λ = 200 Å;

31 - shutter;

32 - sensor angular position and orientation;

33 - image rotation compensator;

34 is a quadratic image detector;

35 - computer for registration and image processing;

36 - algorithmic support of the proposed method is a sequence of operations on registered series of spectrally-filtered, short-exposure images that compensate for atmospheric distortions.

In FIG. 6 is a flowchart of an algorithm for processing registered images and obtaining an undistorted image of the observed space object, where:

37 - selection from a computer memory unit — 35 recorded series of N atmospheric images of an observed space object distorted by the atmosphere;

38 - transformation of each registered image in a Fourier series into the region of its spatial spectrum;

39 — formation of correlation products of spatial spectra of images in “islands” along coherence ellipses and along radial peninsulas;

40 - averaging of correlation products (21) and the formation of double correlations of spatial spectra of images;

41 - phase separation of the averaged correlation products and obtaining differential phases;

42 - stitching of differential phases, restoration of the undistorted phase of the spatial spectrum of the object in the islands and peninsulas in accordance with the equation of one-dimensional stitching of the prototype;

43 - smoothing of all triple products within the islands for all possible triples of closed frequencies;

44 — formation of the equation of closed phases (25) of the triple correlation method;

₀(

;45 - restoration of the phase of the spatial spectrum from the object

₀ (

;

46 - restoration of the square modulus of the spatial spectrum from the object

47 — smoothing within the islands of the mean square modules of the spatial image spectra;

48 — formation of an estimate of the square of the spatial spectrum module of the object undistorted by the atmosphere;

49 - formation of an estimate of the spatial spectrum of the object;

₀ при обратном (20) Фурье преобразовании.50 - obtaining an undistorted atmosphere image of an observed space object

₀ under the inverse (20) Fourier transform.

Let us justify the proposed method and consider its implementation in accordance with the schemes presented in FIG. 1 ÷ 6.

Previous studies (see Bakut P.A., Sviridov K.N., Troitsky I.N., Ustinov N.D. “Study of optimal conditions for recording holograms of intensity and optical images”, Quantum Electronics, v. 2, No. 8 , p. 1688, 1975) indicate that for the effective recognition of objects of observation with a probability of P = 0.998 with a signal-to-noise ratio in the resolution element q = 10, the required number of spatial resolution elements in the image (or, what is also, on the object of observation) must be equal to 100, that is, for an object with dimensions S ₀ = (2x2) m ^{2, the} value of δ of the spatial resolution element of the receiving aperture of the telescope of diameter D _e at a distance to the object R, defined as

= 0,55 мкм требует размера приемной апертуры телескопической системы D_тр = 100 м.should be of the order of δ ≤ δ _tr = 20 cm. A similar resolution of a high-orbit space object at a distance of R = 36000 km at an average wavelength of the optical radiation of the Sun illuminating the object,

= 0.55 μm requires the size of the receiving aperture of the telescopic system D _Tr = 100 m

Obviously, today and in the foreseeable future, the receiving aperture of an optical system with a similar diameter can be created only on the basis of aperture synthesis, capable of combining information from two or more small subapertures with a diameter D <D_tr, extract information about an object with a diffraction resolution characteristic of one large synthesized aperture D_uh ≥ D_tr.

Based on a comparative analysis of existing concepts for constructing optical systems for aperture synthesis, namely, a segmented telescope, a multi-mirror telescope (MZT) and an array of individual telescopes, described, for example, in the book “Optical and infrared telescopes of the 90s”, edited by A. Hunt, ed. Mir, Moscow: 1983, it is obvious that due to technological, operational and financial problems today only a matrix of individual telescopes with bases up to 100 m or more is able to provide the required resolution of small-sized objects of observation.

/D_э основано здесь на комбинировании преддетекторной динамической обработки поля светового информационного сигнала искаженного атмосферой изображения, формируемого при пространственно-временном апертурном синтезе в наземной матрице, и последетекторной статистической обработки модулей и фаз пространственных спектров зарегистрированных в матрице изображений для восстановления модуля и фазы неискаженного атмосферой пространственного спектра наблюдаемого космического объекта.Achieving High Angle Resolution ~

/ D _e here is based on a combination of pre-detector dynamic processing of the field of the light information signal of the image distorted by the atmosphere, formed during space-time aperture synthesis in the ground-based matrix, and post-detector statistical processing of the modules and phases of the spatial spectra of the images recorded in the matrix to reconstruct the module and phase of the spatial atmosphere undistorted by the atmosphere spectrum of the observed space object.

The principle of operation of the claimed method is as follows.

Consider the features of image formation and processing in the proposed method, illustrated in FIG. 1 ÷ 6.

Here the movable telescopes of the matrix - 5 are designed to receive light radiation from the object of observation - 8 from any direction - 9 of the celestial hemisphere, the formation of sub-beams - 5 * and their information in the base station - 6, which, in turn, is intended for coherent combination of sub-beams - 5 * and imaging of the object of observation - 8 at various positions of the moving elements of the matrix - 5.

The movable element of the matrix - 5 telescope of diameter D = 3 ÷ 5 m on a biaxial "alt-alt" mount is placed on a movable base, which must continuously move along the rail track - 7 from the center of the matrix to its periphery with a speed determined by the diameter of the telescope aperture and the number separate short-exposure recordings of images produced for each spatial frequency. So, for example, when the exposure time τ _e = 10 ^-2 s, less than the time of “freezing” of atmospheric turbulences, and the required number of registrations in the series N = 10 ² or 10 ³ , the nominal speed of continuous movement of a telescope of diameter D = 3 m should be, respectively 3 m / s or 0.3 m / s.

~ 5500 Å пропускается дихроическим фильтром - 14 в базовую станую матрицы - 6 для последующего формирования изображения апертурного синтеза. Эта часть света реколлимируется в - 17 до диаметра d = 0,15 м при D = 3 м, то есть масштаб принимаемого телескопом светового излучения χ уменьшается в поперечном сечении в 20 раз. Вследствие ряда отражений, испытываемых субпучком при его доставке к неподвижному фокусу Ф - 13, сжатый пучок диаметра d = 0,15 м при сопровождении объекта наблюдения - 8 вращается вокруг своей оси. Величина поворота пучка однозначно определяется ориентацией телескопа и может быть скомпенсирована надлежащим поворотом К-образного зеркала - компенсатора вращения пучка - 18. В единице подвижного элемента - 5 К-образное зеркало должно осуществлять грубую компенсацию вращения субпучка. Тонкая коррекция эффектов вращения субпучков - 5* выполняется при их комбинировании в базовой станции матрицы - 6, рассматриваемой ниже. После компенсатора вращения реколлимированный параллельный субпучок отражается от зеркал двухосевого стабилизатора его углового положения - 22 и передается через выходной порт подвижного элемента матрицы - 23 вдоль направления его рельсового движения к входному порту базовой станции матрицы - 6. Чтобы обеспечить точное попадание субпучка во входной порт единицы неподвижного элемента, из этого входного порта - 24 к выходному порту подвижного элемента - 23 передается направляющий пучок ИК диапазона, наблюдаемый в подвижном элементе через стабилизатор углового положения пучка - 22 одновременно с реколлимированным субпучком оптического диапазона, который совмещается с ним системой управления стабилизатором углового положения, состоящей из устройств 20 и 21.The construction scheme of the optical-mechanical path (OMT) of the moving matrix telescope - 5 is shown in FIG. 4. It can be seen from it that the light beam from the telescope - 11 of the moving element of the matrix - 5, brought to the focus of F - 13, is split by a dichroic filter - 14, and part of the radiation is reflected in the receiver - 15 of the tracking system for the observation object - 16, and part emission band ∆λ ~ 1000 Å about

~ 5500 Å is passed through a dichroic filter - 14 into the base camp of the matrix - 6 for subsequent imaging of aperture synthesis. This part of the light recolimates at -17 to a diameter of d = 0.15 m at D = 3 m, that is, the scale of the light radiation received by the telescope χ decreases in the cross section by 20 times. Due to a number of reflections experienced by the subbeam during its delivery to the fixed focus F - 13, a compressed beam of diameter d = 0.15 m accompanied by the observation object - 8 rotates around its axis. The magnitude of the beam rotation is uniquely determined by the orientation of the telescope and can be compensated by proper rotation of the K-shaped mirror - beam rotation compensator - 18. In the unit of the movable element - 5, the K-shaped mirror should provide rough compensation of the rotation of the sub-beam. Subtle correction of the effects of rotation of the sub-beams - 5 * is performed when they are combined in the base station of the matrix - 6, discussed below. After the rotation compensator, the recolimized parallel subbeam is reflected from the mirrors of the biaxial stabilizer of its angular position - 22 and transmitted through the output port of the movable matrix element - 23 along the direction of its rail movement to the input port of the matrix base station - 6. In order to ensure that the subbeam accurately hits the input port of the fixed unit element, from this input port - 24 to the output port of the movable element - 23 is transmitted a directing beam of the IR range, observed in the movable element through a hundred the beam angularizer - 22 at the same time as the reclaimed subbeam of the optical range, which is combined with it by the angular position stabilizer control system, consisting of devices 20 and 21.

The fixed element of the matrix is its main and most complex part. It is here that the individual sub-beams - 5 * from the movable telescopes of the matrix - 5 are brought together, aligned at 27 relative to each other in angle (transverse), ensuring their guidance, and along the length of the path в - compensator for the travel differences 25 (longitudinally), ensuring their phasing, and then they are combined in 28, 29 on a common focal plane, providing for their figurization during image formation. The central element (base station) of the matrix - 6 determines and sets the position of the moving elements of the matrix - 5 along the coherence ellipse mentioned above - 7 depending on the angular position - 9 of the observed object - 8. These settings are pairs of moving elements located diametrically opposite to the central element of the matrix , seek, in ensuring the coherence of the matrix, to equalize the length of the traces between the two combined sub-beams. To ensure this rough alignment, the distances between the fixed and moving elements are constantly measured. The exact alignment of the optical path lengths of the combined sub-beams - 5 * is carried out using a path difference compensator - 25. In general, a diagram of the construction of an optical-mechanical path (OMT) of a fixed matrix element is presented in FIG. 5. It can be seen from it that the path difference compensator - 25 is located in one of two combined sub-beams, and the signal for its control is generated using a white light interferometer - 26. This interferometer is powered by two narrow beams of light isolated from the combined sub-beams. The diameters of the order allocated subpuchkov r _0/2 on the receiving apertures - the movable elements 11 of the matrix - 5, and with the scale factor χ subpuchkov they are equal to r ₀ / 2χ = 2,5 mm, with χ = 20 and r ₀ = 10 cm.

The initial phasing of the sub-beams of the path difference compensator - 25 should be performed when the moving elements of the matrix - 5 are stationary after their rough installation along the minimum coherence ellipse - 7. Upon reaching alignment for all pairs of the sub-beams of the matrix - 5, the moving matrix telescopes begin their movement to provide an aperture synthesis. To form images of deep space objects in an aperture synthesis system with a diameter of D _tr = 100 m and f / 100, it is necessary to carry out large-scale modeling during figurization in the sense that real aperture is 29, focusing the sub-beams and forming images, has a diameter of D _em = 1 m, i.e. 100 times smaller than with the equivalent focal distance F _e = 100 m, to ensure proper scale modeling combinable subpuchki compressed in rekollimatorah - 17 the movable elements of the matrix - 5 to 20 times, should be even further reduced cross section is 5 times. Reduced in the fixed element - 6 to a diameter of 0.03 m, the sub-beams are sent through compensators for their trembling - 27 to the corresponding shoulders of the periscope system - 28, which provides scaling of their relative positions, and from it are sent to the aforementioned mirror focusing system - 29 of diameter D _em = 1 m with equivalent focus F _e = 100 m

To ensure the correct transverse combination of the sub-beams and the superimposition of their sub-images, as well as for their correct orientation relative to each other, the fixed matrix element contains in each arm an image shake compensator - 27 and an image rotation compensator - 33. To ensure the operation of these compensators, a part of the focused radiation is separated by dichroic filter - 30 and is sent to the focal plane of the tracking system for the angular position of the sub-images and their orientation - 32. In this case, the dichroic filter o there is spectral filtering and passes a narrow band Δλ = 200 Å for the formation of the image, and the remainder of the radiation in the band 1000 Å deviates to the detector of the servo system - 32. Using a high-speed shutter - 31 near the detector of the servo system, which allows you to alternately observe each of the combined sub-beams, or rather their sub-images, you can estimate the angular position errors of each of the sub-images, and then compensate them by adjusting the mirrors of the jitter compensator - 27 in the channel of this subbeam.

To ensure the correct orientation of the combined sub-beams and the generated sub-images, it is necessary to correct the errors of any residual rotation of the sub-beams around their axis during tracking of the observation object - 8. To do this, slowly move the telescopes - 5 and, alternately locking the shutter - 31 focusable sub-beams, observe the swings of the corresponding subimages. The amplitude of the swings can be, for example, within a few angular seconds, and the sway direction of the sub-image is controlled by the corresponding compensator for rotation of the images with a K-shaped mirror - 33 by the base station of the matrix - 6 so that the swings of the subimages from different movable telescopes are carried out along the same or, at least parallel lines. After performing the indicated corrections in the orientation and position of the sub-beams, the aperture synthesis system under consideration is generally ready to detect the generated images in a quadratic image detector - 34 and register them and process them in a computer for image registration and processing - 35.

In space-time aperture synthesis, a continuous change in the mutual position of the moving telescopes of the matrix - 5 relative to each other and relative to the base station of the matrix - 6 takes place. Consider the dynamics of this change during the formation of images distorted by the atmosphere.

In the initial position for observation, the movable telescopes of the matrix - 5 are installed along the coherence ellipse - 7, determined by the position - 9 of the object - 8 relative to the aperture synthesis matrix. Moving the matrix’s movable telescopes from the initial position should be carried out so that they, moving radially, are constantly along the corresponding coherence ellipses - 7, which provides coarse phasing and reduces the range of adjustment of the path difference compensator - 25. Therefore, the motion of the matrix telescopes - 5 should be synchronous and in one direction. Considering that during image restoration, the unfolding of the phase of the spatial spectrum is carried out from the region of low spatial frequencies to the region of high spatial frequencies, in order to enable simultaneous implementation of image acquisition and processing processes, the motion of the matrix telescopes is carried out from the center of the matrix to its periphery. Having chosen the direction of motion, determining the direction - 9 to the object - 8 and positioning the moving matrix elements along the coherence ellipse - 7 with a minimum distance to the fixed matrix element - 6, equal to the diameter of the aperture D of the moving element (L _min = 2D) in the presence of coherence of subbunches characterized by by the presence of interference bands in the image, they begin to detect in 34 series of spectrally-filtered in a dichroic filter with a passband Δλ = 200 Å (30) short-exposure images of the observed space object a.

If we talk about discrete installations of moving matrix elements, then, for example, for a system for observing deep space objects, there should be so many that in the reconstructed image of a geostationary satellite there should be at least 100 resolution elements mentioned above. Considering that the required number of spatial spectrum samples is equal to the required number of resolution elements of the reconstructed image, we find that for the considered matrix of diameter D _e = 100 m there should be at least 10 samples along any diameter, i.e. at least 5 samples along each radius. To obtain these samples, the positions of the moving elements of the matrix could be set in discrete steps at intervals of 10 m. However, to avoid jolts when changing the modes of motion, it is advisable to work with continuously moving telescopes - 5 and constant monitoring of the ellipticity of their connecting line - 7, determined by the position - 9 of the object - 8. Let us evaluate the characteristics of this movement.

The moving elements of the matrix - 5 will continuously move, so that in each frame of the image a slightly different set of spatial frequencies is detected. Due to the fact that for each spatial frequency an average of N = 10 is required⁵exposures, in order to achieve the maximum resolution during processing, the speed of the movable matrix telescopes must correspond to a displacement of D = 5 m in one hundred thousand exposures of 10 ms duration, i.e., this speed is 5 · 10^-3 m / s With this speed, the moving elements of the matrix - 5 will move from the initial position along the minimum ellipse of coherence - 7 at the base station of the matrix - 6 in the center of the matrix to its periphery until the separation between the pairs of moving elements - 5 located diametrically opposite to the base station of the matrix is 6, will not reach the value L_m, corresponding to the required resolution, determined by the angular size of the object of observation and the acceptable time of aperture synthesis. It should be noted that during continuous motion, the matrix has a continuous peninsular OPF in radial directions, which reduces the level of the side lobes of its PSF and increases the field of view of the matrix, and the island OPF along coherence ellipses, which facilitates phase closure by the triple correlation method considered below.

The total exposure time of the images acquired in the matrix is determined by the maximum achievable resolution and the speed of movement of the moving telescopes of the matrix. The maximum achievable resolution in the case of observation of deep space objects under consideration sets the maximum distance of 50 m that each movable aperture of the matrix must travel at the maximum distance between diametrically opposite apertures L _max = 100 m. When the speed of the moving telescope of the matrix is 5, equal to V _t = 5 10 ^-3 m / s at N = 10 ⁵ exposures at each spatial frequency, also determined by the limiting resolution, the total time of aperture synthesis and acquisition of images of an object will be

(at N = 10 ⁷ , V _T = 5 · 10 ^-5 m / s, T = 280 hours = ~ 12 days)

For geostationary satellites in synchronous orbits, due to their low apparent angular velocity of movement, we can theoretically have unlimited time for observation and, therefore, acquisition of the required number N of short-exposure images. Thus, the required aperture synthesis time (2) is not a limiting factor in solving the problem of observing small-sized objects in deep space.

So, having formed and registered in the computer - 35 a series of distorted images of the observation object, we consider the features of processing the recorded images in the proposed method for reconstructing the undistorted phase and the spatial spectrum modulus of a small space object and obtaining its undistorted image.

The triple correlation method mentioned above is a promising method for reconstructing the phase of the spatial spectrum from an object from a series of short-exposure images distorted by the atmosphere in terrestrial multi-aperture optical systems. This method is described in A.W. Lohmann, G. Weigelt, B. Wirnitzer, Appl. Opt., V. 22, p. 4028, 1983 and is based on the formation of triple correlation of images defined by

and obtaining a Fourier transform from (3) the spatial spectrum of a triple correlation, called the bispectrum.

(

) - пространственный Фурье спектр изображения I_и(

), а пространственные частоты

₁,

₂ и -

₁ -

₂ образуют замкнутую тройку.where =

(

) - spatial Fourier spectrum of the image I_and(

), and spatial frequencies

_one,

₂and -

_one-

₂form a closed triple.

Averaging the bispectrum over a series of recorded images and isolating its phase, we obtain the equation of closed phases in the form

This equation allows, using the algorithm for unfolding the equations of closed phases, to restore the phase of the spatial spectrum of the object from the measured phase of the bispectrum of the image, as described in H. Bartelt, A.W. Lohmann, B. Wirnitzer "Phase and amplitude recovery from bispectra", Appl. Opt., V. 23, p. 3121, 1984.

Consider a modification of the triple correlation method proposed in this method for observing small-sized space objects.

/D. При этом

пространственный спектр от объекта

практически не изменяется в пределах островов, создаваемых парами субапертур при каждом короткоэкспозиционном измерении, и для D > r₀ можно существенно (в N_θ = (D/r_o)² раз) повысить точность оценки фазы

методом тройных корреляций, а также улучшить оценку модуля

пространственного спектра от объекта, получаемую по методу Лабейри (аналог).A typical situation for space observation problems is when the angular dimensions of the object θ ₀ are smaller than the angular resolution of individual subapertures, defined as

/ D. Wherein

spatial spectrum from the object

practically does not change within the islands created by pairs of subapertures during each short-exposure measurement, and for D> r ₀ it is possible to significantly (in N _θ = (D / r _o ) ² times) increase the accuracy of phase estimation

triple correlation method, and improve the module estimate

spatial spectrum from the object, obtained by the Labeiree method (analogue).

областей корреляции атмосферных искажений.Indeed, we consider three redundantly located, but excessively large subapertures, such that each of them fits into

areas of correlation of atmospheric distortions.

является постоянным в пределах каждого острова размера 2D/

и равным

где

- центральная частота острова, то перед корреляционным усреднением (5) можно сгладить все тройные произведения (4) в пределах островов по всем возможным тройкам замкнутых частот, то есть осуществить интегрирование видаIf now, in accordance with the small size of the object, assume that

is constant within each island of size 2D /

and equal

Where

is the central frequency of the island, then before the correlation averaging (5) it is possible to smooth out all ternary products (4) within the islands over all possible triples of closed frequencies, i.e., integrate the form

where integration is carried out over the corresponding islands of the spatial frequency domain. Then the equation of closed phases of the triple correlation method, taking into account (6), is transformed to

=

) - фазы пространственного спектра от объекта на m островах.Where

=

) are the phases of the spatial spectrum from the object on m islands.

Let us evaluate the accuracy of the known (5) and proposed (6) methods within the framework of the Kolmogorov-Obukhov atmospheric distortion model. The accuracy of the estimate is the reciprocal of the signal-to-noise ratio, which characterizes the recovery efficiency and is determined by the following value

where N is the number of processed short exposure images in the series, and the angle brackets <·> indicate the full statistical averaging both in quantum statistics of the detection process and in statistics of atmospheric distortions.

For the well-known triple correlation method (5), averaging in (8) over the statistics of quanta and over atmospheric distortions in the asymptotics D >> r₀, we get an expression for the accuracy of phase recovery

where the parameter q () makes sense of the signal-to-noise ratio in one image and is determined

and the parameter η characterizes the number of quanta arriving at one “speckle” of the image or, which, also, at the correlation region of distortions in the aperture plane, and is determined

where <K> is the average number of detected photons per image, and M is the number of mobile telescopes in the matrix.

Obviously, two extreme cases can be distinguished here:

1) bright objects η >> 1 (q >> 1) and

2) weak objects η << (q << 1),

a) then in the classical case of observing bright space objects, we have

b) in the quantum-limited case of observing weak objects, we have

нетрудно видеть, что в тройном произведении (5) порядка

полезных членов на замкнутых частотах и около

шумовых слагаемых со случайной фазой. Поэтому отношение сигнал/шум в (12) и (13) было пропорционально

Let us evaluate the effectiveness of the proposed modification (6) of the triple correlation method in comparison with the traditional triple correlation method (5). Based on the N _θ phase cell model

it is easy to see that in the ternary product (5) of order

useful members at closed frequencies and around

noise terms with random phase. Therefore, the signal-to-noise ratio in (12) and (13) was proportional

тройным произведениям спектров и, в результате, полезных членов становится ~

, и случайных шумовых ~

, а отношение сигнал/шум в (12) и (13) становится пропорциональным

и может быть представлено в видеNow, integration in the proposed method (6) is equivalent to summation over

triple products of spectra and, as a result, useful terms becomes ~

, and random noise ~

, and the signal-to-noise ratio in (12) and (13) becomes proportional

and can be represented as

a) for bright space objects (η >> 1)

b) for weak space objects (η << 1)

Note that similar smoothing (6) within the islands is necessary to carry out to obtain an estimate of the square of the modulus of the spatial spectrum from the object, which is then defined as

- дифракционная ОПФ матрицы, интегралы берутся в пределах островов, а отношение сигнал/шум (8) преобразуется к видуHere

- diffraction OPF matrix, the integrals are taken within the islands, and the signal-to-noise ratio (8) is converted to

a) for bright objects (η >> 1)

b) for weak objects (η << 1)

раз требуемое число приобретаемых изображений. Точность восстановления увеличивается с ростом диаметра субапертуры D, но до тех пор, пока удовлетворяется неравенство

Based on the results obtained (12) ÷ (18), we can conclude that when observing small-sized objects, the matrix functioning efficiency increases (D / r _o ) ² times. The accuracy of reconstruction of the module and the phase of the spatial spectrum from the object is increased, which reduces

times the required number of acquired images. The accuracy of the restoration increases with increasing diameter of the subaperture D, but until the inequality

/D_э, определяемого размером синтезируемой апертуры D_э. The positive effect of using the inventive method is to ensure coherent combination (guidance, phasing and figure) of the sub-beams from individual subapertures of diameter D of the movable matrix telescopes to achieve high angular resolution

/ D _e, defined by the aperture size of the synthesized D _e.

The coherent operation of the matrix of mobile telescopes during the aperture synthesis provides a gain in diffraction resolution in D_uh/ D times (D_uh/ D >> 1) in comparison with a single-aperture optical system for observing space of diameter D.

For example, when observing deep space objects with D_uh= 100 m and D = 5 m, this gain in resolution is 20 times.

Another positive effect of the use of the proposed method is to increase the accuracy of reconstruction of the atmosphere-undisturbed module and phase of the spatial spectrum from an object by (D / r ₀ ) ² times the proposed smoothing procedure in the islands in comparison with traditional methods of module reconstruction by the Labeiri method (analogue) and phase triple correlation method.

For example, with D = 5 m and r ₀ = 0.1 m, this gain is 2500 times and allows the required number N of registrations in the series to be reduced by the same amount, reducing the total observation time (2).

In accordance with the proposed algorithm - 36 processing registered in the computer - 35 series of N atmosphere-distorted images of the observed space object carry out the following sequence of operations:

37) choose from the computer memory block - 35 registered series of N images of the observed space object distorted by the atmosphere

obtained for each Kth relative position of the moving telescopes of the matrix (k = 1, 2, ....... K);

38) transform each registered image in the Fourier series into the region of its spatial spectrum

(

неискаженной атмосферой пространственный спектр объекта, а

мгновенная ОПФ системы атмосфера-матрица для

-той регистрации и k-го расположения элементов матрицы;Where

(

undistorted atmosphere the spatial spectrum of the object, and

instant atmospheric-matrix opf for

-th registration and k-th arrangement of matrix elements;

39) form the correlation products of the spatial spectra of images in the “islands” along the coherence ellipses and along the radial peninsulas

40) average correlation products (21) and form double correlations of spatial image spectra

41) isolate the phase of the averaged correlation products and get the differential phase

42) stitching the differential phases, restore the undistorted phase of the spatial spectrum of the object in the islands and peninsulas in accordance with the equation of one-dimensional crosslinking of the prototype

- узловые частоты на выбранном контуре «сшивания»

Where

- nodal frequencies on the selected loop "stitching"

Using the one-dimensional stitching algorithm (24), it is possible to expand the phase of the spatial spectrum from an object only within each island or radial peninsula.

In order to relate the phases of islands or peninsulas over the entire space-frequency region of aperture synthesis, it is proposed to use the triple correlation method (3) with the equation of closed phases of the form (5)

₀<

D) перед корреляционным усреднением (25) ≡ (5) сглаживают все тройные произведения в пределах островов по всем возможным тройкам замкнутых частот, то есть осуществляют интегрирование (26) вида43) given the small size of the object of observation (

₀ <

D) before correlation averaging (25) ≡ (5), all triple products within the islands are smoothed over all possible triples of closed frequencies, i.e., they integrate (26) of the form

44) taking into account (26) ≡ (6) form the equation of closed phases (25) of the triple correlation method in the form

- фазы пространственного спектра от объекта на

m островах.Where

- phases of the spatial spectrum from the object to

m islands.

разворачивая уравнение замкнутых фаз (27) в соответствии с рекурсивным соотношением45) restore the phase of the spatial spectrum from the object

expanding the equation of closed phases (27) in accordance with the recursive relation

(

_s,

_h) фаза биспектра с учетом сглаживания (26),

а скобки [·] - обозначают целую часть.Where

(

_s

_h ) bispectrum phase, taking into account smoothing (26),

and brackets [·] - indicate the integer part.

₀(

₁) полагается равной нулю, а на h-ом шаге фаза

₀(

_h) выражается через фазы, оцененные на предшествующих шагах с помощью

соотношений типа (27).In the first step, the phase

₀ (

₁ ) it is assumed to be zero, and at the hth step, the phase

₀ (

_h ) expressed through phases evaluated in the previous steps with

relations of the type (27).

₀ восстанавливают квадрат модуля пространственного спектра от объекта

для чего сначала по зарегистрированным сериям искаженных изображений объекта, а точнее по их пространственным спектрам, формируют средний квадрат модуля пространственных спектров изображений как46) simultaneously with the restoration of the phase of the spatial spectrum from the object

₀ restore the square of the modulus of the spatial spectrum from the object

why first, according to the registered series of distorted images of the object, and more precisely according to their spatial spectra, form the average square of the module of the spatial spectra of the images as

аналогично (6), осуществляют сглаживание в пределах островов средних квадратов модулей пространственных спектров изображений47) given the small size of the object of observation

similarly to (6), smoothing within the islands of the mean square modules of the spatial spectra of images

48) and form an estimate of the undistorted by the atmosphere square modulus of the spatial spectrum of the object as

- дифракционная ОПФ матрицы для k-го расположения ее подвижных элементов, а интегралы берутся в пределах

островов.Where

- diffraction OPF matrix for the k-th location of its moving elements, and the integrals are taken within

islands.

49) according to the restored estimates of the phase and the spatial spectrum modulus from the object, an estimate of the spatial spectrum of the object

₀ при обратном (20) Фурье преобразовании от

50) receive an undistorted atmosphere image of the observed space object

₀ with the inverse (20) Fourier transform of

Thus, the proposed method for obtaining images of space object observed through a turbulent atmosphere, allows to increase the diffraction resolution of formed images in D _e / D time and accuracy of reconstruction undistorted module atmosphere and phase spatial spectrum object (D / r ₀₎ ² times, thus providing the possibility of effective visual monitoring of the state of geostationary space objects and devices of the GLONASS system in the conditions of a possible failure of telemetric communication channels, and also allows to control small space debris of natural (asteroid-comet) origin.

Claims (1)

A method of obtaining images of a space object observed through a turbulent atmosphere,
based on the formation of a terrestrial image of a space object by a ground-based optical system,
their spectral filtering and quadratic detection of each during the exposure time, less than the interval of time correlation of atmospheric fluctuations,
registration of series of N such spectrally filtered, short exposure images,
transforming each of them according to Fourier into the region of the spatial spectrum
and the statistical processing of the modules and phases of the spatial spectra of the recorded images of the series for restoring the atmosphere undistorted module and phase of the spatial spectrum of the observed space object,
the formation on them of the spatial spectrum of the object, undistorted by the atmosphere, and obtaining, with the inverse Fourier transform, the image of the observed space object, undistorted by the atmosphere, from it, characterized in
that the formation of atmospheric images of a space object distorted by the atmosphere is carried out by a coherent matrix of M ground-based mobile telescopes of diameter D in the process of space-time aperture synthesis,
in which at first the individual matrix telescopes are arranged in a circle at the center of the matrix, if the object is at the zenith, or along the coherence ellipse, which is the intersection of the aperture synthesis plane with the rotation paraboloid aimed at the oblique observation object,
then, to obtain a series of independent, spectrally-filtered, short-exposure images of the observed space object, synchronous movement of the matrix’s moving telescopes from its center to the periphery is carried out, preserving their relative position along coherence ellipses,
and to ensure smooth movement and eliminate jolts, continuous movement of the matrix telescopes along rail tracks extending radially from the center of the matrix to its periphery,
while the orientation of each matrix telescope relative to the center of the matrix is maintained unchanged and the combined sub-beams are directed from movable telescopes along rail tracks to the center of the matrix,
where a fixed base station is located, in which both the coherent combination of radially propagating sub-beams during the aperture synthesis of the generated images and the quadratic detection of the generated and spectrally filtered images are carried out, with their subsequent registration and processing,
while registering a series of N spectrally-filtered, short-exposure images of the observed space object for each relative position of the moving telescopes of the matrix,
in the statistical processing of the modules and phases of the spatial spectra of a series of recorded images distorted by the atmosphere, use the island nature of the optical transfer function (OPF) of the matrix along the coherence ellipses and its OPF peninsula in the radial direction, extending from the center of the space-frequency region to the cutoff frequency of the synthesized aperture of diameter D _E , and restore the atmosphere-undistorted phase of the spatial spectrum from the object in the islands and peninsulas, deploying it from the center to peripherals
radially reconstructed phases are stitched together over the entire spatial frequency region of the aperture synthesis using the triple correlation method with unfolding the equations of closed phases along coherence ellipses, while for small space objects not resolvable by individual matrix telescopes before correlation averaging of statistical processing, all triple products within the islands are smoothed out for all possible triples of closed frequencies and,
by performing a similar smoothing during statistical processing of the squares of the spatial spectrum moduli of the recorded images, the phase and the spatial spectrum modulus of the object are undistorted by the atmosphere,
combining these, they form the spatial spectrum of the object and, when the Fourier transform is inverse, they obtain an undistorted image of the observed space object from the atmosphere.

Images