RU2629925C1 - Method of obtaining and processing images of remote earth sensing distorted by turbulent atmosphere - Google Patents

Abstract

FIELD: physics.

SUBSTANCE: invention relates to the method of obtaining and processing images of Earth remote sensing (RES) distorted by a turbulent atmosphere. The method includes obtaining, in a wide field of view, one spectrally filtered short-exposure image of the RES spatially noninvariant to atmospheric distortions, statistical processing of its isoplanatic sub-images and their fragments, determining the instantaneous optical transfer functions of the atmosphere system - the RES telescope for each isoplanatic region of each sub-image of the registered RES. The obtained data are used for the subsequent spatial filtration of the corresponding sub-images and for combining the results of the filtration of the sub-images in one frame for the reconstruction of the diffraction-limited object of the remote Earth sensing - extended non-isoplanatic portion of the probed Earth surface - undistorted by the atmosphere.

EFFECT: simplifying and accelerating the process of obtaining images and improving the quality of images.

2 dwg

Description

The claimed invention relates to the field of optical instrumentation and is intended for rapid acquisition and digital restoration of an undistorted image of the object — an extended portion of the probed earth’s surface that is spatially non-invariant to atmospheric distortions.

Let us consider the features of the influence of a turbulent atmosphere on Earth remote sensing systems (ERS).

The presence of a turbulent atmosphere of the Earth between the probed portion of the Earth’s surface and the remote sensing spacecraft significantly limits the information capabilities of remote sensing systems. Two problems arise: the problem of “seeing” through a turbulent atmosphere and the problem of “isoplanarity” of the atmosphere-telescope remote sensing system [1] (KN Sviridov Technologies for achieving high angular resolution of optical atmospheric vision systems. M .: Knowledge, 2005).

The essence of these problems is that the problem of “vision” imposes restrictions on the minimum size of parts resolved by the atmosphere-telescope remote sensing system on the probed portion of the earth’s surface, and the problem of “isoplanarity” limits the maximum size of the probed portion of the earth’s surface, which is still spatially invariant to atmospheric distortions, that is, this problem limits the field of view of the atmosphere-telescope remote sensing system.

These problems depend significantly on the observation conditions, and, in particular, on the conditions for the registration of remote sensing images.

If the time of registration (exposure) τ _E exceeds the interval of the temporal correlation of atmospheric fluctuations τ _A (the so-called time of “frozen” turbulence of the atmosphere), we speak of long-exposure registration, and if the time of registration τ _{E is} less than τ _A , then we speak of short exposition registration. These two extreme cases differ significantly in the nature of atmospheric distortions. So, if a long exposure image averaged over atmospheric distortions for a time τ _E > τ _A has a lower resolution than an instantaneous short exposure image recorded for a time τ _E <τ _A , then it is spatially invariant to atmospheric distortions during to all, the field of view of the atmosphere-telescope remote sensing system, in contrast to the short-exposure image, consisting in this field of a series of instantaneous isoplanatic regions that are spatially non-invariant to atmospheric distortions.

In accordance with these features of the effect of atmospheric turbulence on Earth remote sensing systems at an early stage in the development of Earth remote sensing technologies, the desire to work in a wide field of view stimulated the acquisition of long-exposure images of Earth remote sensing, as in the domestic spacecraft of Earth remote sensing:

“Resource-DK1” [2] (Petri G. Russian satellite “Resource-DK1”: an alternative source of ultra-high resolution data. Geomatics, No. 4, pp. 38-42, 2010) and

“Resource-P” [3] (Kirilin AN and others. The spacecraft “Resource-P.” Geomatics, No. 4, pp. 23-26, 2010), and

in American remote sensing spacecraft: “Quick Bird”, “World View”, and “Geo Eye” [4] (Lavrov VV Space-based film-making systems of ultra-high resolution. Geoinformation portal of the GIS Association, No. 2, 2010).

These publications [2, 3, 4] we will consider here, as analogues of the proposed method in terms of image acquisition. The time delay and accumulation (WZN) technology used in them for detection leads to the recording of a long-exposure remote sensing image averaged over atmospheric distortions.

A disadvantage of the existing technologies [2, 3, 4] for remote sensing of the Earth, which we consider as analogues of image acquisition, is the lack of any processing in them that corrects the atmospheric distortions of the recorded long-exposure image.

With the development of remote sensing technology, new technologies have appeared that allow to determine and correct atmospheric distortions. These technologies can conditionally be attributed to two classes: hardware and algorithmic technologies. Consider these analogues of the method proposed here.

- пространственный радиус корреляции атмосферных флуктуаций светового излучения на высоте Н космического аппарата ДЗЗ, а

- средняя длина волны солнечного излучения подсвета земной поверхности

. Эта технология, исследованная в работе [5] (Свиридов К.Н. О предельном разрешении аэрокосмических систем дистанционного зондирования Земли (ДЗЗ). Журнал «Ракетно-космическое приборостроение и информационные системы», т. 1, вып. 1, с. 34, 2014), позволяет в условиях атмосферного «видения» и при длинно-экспозиционной регистрации изображений ДЗЗ достигать предельного разрешения, равного 4,6 см. Недостаток этого аналога заключается в трудности его практической реализации, так как он требует создания телескопа апертурного синтеза концепции МЗТ (многозеркального телескопа) с диаметром апертуры: D=7м при Н=350 км; D=10м при Н=500 км и D=15 м при Н=750 км.The first hardware technology for increasing the spatial resolution of remote sensing systems is based on changing a remote sensing telescope, namely, replacing a glass telescope-refractor, domestic remote sensing telescopes [2, 3] with mirror reflecting telescopes [4], and most importantly, increasing the diameter of the receiving aperture of the telescope D to the value D> 2r ₀ (λ, H). Here

- the spatial radius of the correlation of atmospheric fluctuations of light radiation at a height H of the remote sensing spacecraft, and

- the average wavelength of solar radiation illuminating the earth's surface

. This technology, studied in [5] (Sviridov KN On the maximum resolution of aerospace remote sensing systems of the Earth (ERS). Journal "Rocket and Space Instrumentation and Information Systems", t. 1, issue 1, p. 34, 2014), allows in conditions of atmospheric "vision" and long-exposure registration of remote sensing images to reach a maximum resolution of 4.6 cm. The disadvantage of this analogue is the difficulty of its practical implementation, since it requires the creation of an aperture synthesis telescope for the MZT concept (many telescope) with an aperture diameter: D = 7m at H = 350 km; D = 10m at H = 500 km and D = 15 m at H = 750 km.

определяется соотношениемIn accordance with studies conducted in [5], the quantity

determined by the ratio

- величина пространственного радиуса корреляции атмосферных флуктуации светового излучения на границе турбулентного слоя L (L≈10 км). Отсюда видно, что при H=350 км

оказывается равной 3,5 м, при Н=500 км

, и при Н=750 км величина

оказывается равной 7,5 м. Полученные значения

, во-первых, объясняют требуемые величины диаметров для телескопов ДЗЗ апертурного синтеза: D=7, 10 и 15 м, и, во-вторых, оказываются существенно большими диаметра D=1,1 м существующих телескопов ДЗЗ [4]. Поэтому атмосферные искажения волнового фронта светового излучения на приемной апертуре телескопа ДЗЗ представляют собой случайные наклоны волнового фронта.Where

- the value of the spatial radius of the correlation of atmospheric fluctuations of light radiation at the boundary of the turbulent layer L (L≈10 km). This shows that at H = 350 km

It turns out to be equal to 3.5 m, at H = 500 km

, and at Н = 750 km the value

It turns out to be equal to 7.5 m. The obtained values

firstly, they explain the required diameters for remote sensing telescopes of aperture synthesis: D = 7, 10 and 15 m, and secondly, they turn out to be significantly larger diameters D = 1.1 m of existing remote sensing telescopes [4]. Therefore, atmospheric distortions of the wavefront of light radiation at the receiving aperture of a remote sensing telescope are random tilts of the wavefront.

система с адаптивной компенсации случайных наклонов волнового фронта по сравнению с системой без компенсации обеспечивает максимальный выигрыш разрешения в 4 раза [7]. Недостаток этого аналога предлагаемого здесь способа, как и предыдущего аналога, заключается в том, что, хотя аппаратурные технологии обеспечивают потенциально хорошие результаты по разрешению, но они требуют существенной модернизации аппаратуры систем ДЗЗ.This circumstance led to the development of a new hardware technology for increasing the spatial resolution of remote sensing systems. It is based on pre-detector adaptive compensation of the above-mentioned random wavefront tilts caused by the influence of a turbulent atmosphere during the time of “frozen” atmospheric turbulence τ _A. This technology (analogue) was proposed in [6] (Sviridov K.N., Volkov S.A. Method of remote sensing of the Earth. Application for invention RU2015129353 dated 07.17.2014, the applicant - JSC “Russian Space Systems”) and studied in [7 ] (Sviridov KN Remote sensing of the Earth with adaptive compensation of random tilts of the wave front. Journal “Rocket and space instrument making and information systems”, vol. 2, issue 3, p. 12, 2015). This remote sensing method allows you to obtain an average short-exposure image. Its average short-exposure optical transfer function (OPF) prevails over the average OPF of the long-exposure image in the entire range of spatial frequencies, providing a gain in the resolution of the average short-exposure remote sensing image. Studies have shown that with an optimal aperture diameter of the remote sensing telescope equal to

a system with adaptive compensation of random wavefront tilts in comparison with a system without compensation provides a maximum resolution gain of 4 times [7]. The disadvantage of this analogue of the method proposed here, as well as the previous analogue, is that, although the hardware technologies provide potentially good resolution results, they require a significant modernization of the equipment of remote sensing systems.

An easier way to achieve positive results in improving spatial resolution and increasing the isoplanatic field of view of remote sensing systems is provided by algorithmic technologies.

Consider two algorithmic technologies, one of which we will consider as an analogue, the other as a prototype of the method proposed here.

As an analogue of the proposed method, we take an algorithmic technology for increasing the spatial resolution of remote sensing images, proposed in [8] (Sviridov K.N. A method for obtaining and processing images distorted by a turbulent atmosphere. Application for invention RU 2016100934 dated 01/14/2016, the applicant is Russian Space systems "). This technology does not require a change in the detection strategy for WZV and is based on post-detector adaptive filtering of the recorded long-exposure remote sensing image that is spatially invariant to atmospheric distortions in the entire field of view of the atmosphere-telescope remote sensing system. Studies [9] (KN Sviridov Adaptive filtering of medium images distorted by a turbulent atmosphere. The rocket-space instrument making information systems journal, vol. 2, issue 4, p. 40, 2015) confirmed the effectiveness of adaptive filtering -exposure image to increase its spatial resolution. Moreover, it was found that the gain in resolution does not exceed 2 times, but this gain may be sufficient to increase the spatial resolution of domestic remote sensing data, which is today 1 m, to a foreign level of spatial resolution, which is today 0.5 m.

Another algorithmic technology of remote sensing, taken as a prototype, was proposed in [10] (Sviridov KN Remote Sensing of the Earth (Remote Sensing). Patent for invention RU2531024 dated 08/08/2014 by application RU 2013125540 dated 06/03/2013, applicant and patent holder - JSC “Russian Space Systems”) and is based on the receipt and processing of a series of N spectrally-filtered short-exposure images of remote sensing. Research [11] (KN Sviridov On a new approach to obtaining and processing remote sensing images distorted by a turbulent atmosphere. The rocket-space instrument making and information systems journal, vol. 1, issue 4, p. 28, 2014) showed that as a result of a series of instantaneous remote sensing images independent of each other by atmospheric distortions, and their subsequent fragmentary statistical processing, the average short-exposure image is restored, characterized by the resolution of the average short-exposure OPF, and zoplanatichnosti sight average BPA long-exposure image. Thus, the prototype allows you to increase spatial resolution while increasing the spatially invariant field of view of remote sensing systems.

The disadvantages of the prototype include, firstly, the complexity of the practical implementation, which is due to the need to change the process of detecting remote sensing images and the transition from traditional detection of medium long-exposure images of the WZN strategy to the strategy of selective detection of instantaneous short-exposure remote sensing images, independent of each other atmospheric distortion. The second disadvantage of the prototype is the increased time to obtain the initial processing for a series of N instantaneous images, due to the aforementioned strategy for the selective detection of independent images.

To eliminate the noted disadvantages of the prototype, this method is proposed, based on obtaining in a wide field of view a single spectrally-filtered, short-exposure image of a remote sensing image that is spatially non-invariant to atmospheric distortions, statistical processing of its isoplanatic subimages and their fragments, a posteriori determination of instantaneous OPF of the atmosphere Remote sensing telescope for each area of isoplanarity (each subimage) of the original remote sensing image, their use for subsequent space filtering the corresponding sub-images and combining the results of filtering the sub-images in one frame to restore the undistorted atmosphere of a diffraction-limited remote sensing object.

The technical result of the proposed method is to simplify and accelerate the process of obtaining remote sensing images in a wide spatially non-invariant field of view of the atmosphere-telescope remote sensing system, and most importantly, restoring an undistorted image of the remote sensing image with diffraction resolution of the remote sensing telescope in its wide field of view.

The technical result is achieved by the fact that on board the remote sensing spacecraft receive in the wide field of view of the remote sensing telescope one spectrally-filtered (Δλ≤Δλ _A = 250 A ⁰ ) short-exposure (τ _E ≤ τ _A = 1 ms) image of the object - an extended section probed earth's surface, spatially non-invariant to atmospheric distortions, and

transmit it via a radio link to the Earth for digital processing, in which the size of the instantaneous isoplanarity region of the atmosphere-telescope system in the recorded image is first determined and

, соизмеримых с элементом разрешения системы атмосфера-телескоп, затемN subimages I _and ^j are distinguished in it, commensurate with the size of the isoplanatic region, and M fragments are distinguished in each subimage

commensurate with the resolution element of the atmosphere-telescope system, then

и

, гдеtransform every j-th subimage and every ij-th fragment according to Fourier into the region of their spatial spectrum

and

where

и фазы

полученных MN пространственных спектров

и одновременно осуществляют их раздельную статистическую обработку, для чегоhighlight the squares of the modules

and phases

obtained MN spatial spectra

and simultaneously carry out their separate statistical processing, for which

, затемfirst, the squares of the spatial spectrum moduli M of the image fragments are averaged over i and the average square of the spatial spectrum modulus of the image fragments within the jth subimage is obtained

then

, далееlikewise, the squares of the spatial spectrum moduli of N image fragments are averaged over j and the average square of the spatial spectrum modulus of the image fragments is obtained over N sub-images

, Further

, являющийся для заданных условий наблюдения аналитически известным, и,form the average square of the OPF module of the atmosphere-telescope system

being analytically known for given observation conditions, and,

,using it for inverse filtering of the average square of the modulus of the spatial spectrum of image fragments averaged over N subimages

,

,get the average square modulus of the spatial spectrum of the fragments of the object, averaged over N subimages

,

Further considering the statistical homogeneity of the object DZ3-probed plot of the earth’s surface,

, к среднему квадрату модуля пространственного спектра фрагментов объекта, усредненному по М фрагментам j-го субизображения

иequate the average square modulus of the spatial spectrum of fragments of an object averaged over N sub-images

, to the average square of the modulus of the spatial spectrum of the object fragments averaged over M fragments of the j-th subimage

and

для инверсной фильтрации среднего квадрата модуля пространственного спектра фрагментов изображения, усредненного по i в пределах j-того субизображения

,use it

for inverse filtering of the mean square modulus of the spatial spectrum of image fragments averaged over i within the jth subimage

,

restoring the square of the module of the instantaneous OPF of the atmosphere-telescope system for the j-th subimage, and,

,extracting the square root from it, we obtain the instantaneous OPF module for the jth subimage

,

по i, то есть в пределах j-того субизображения, иat the same time, to restore the phase of the instantaneous OPF of the j-th subimage, the phases of the spatial spectra of image fragments are first averaged

by i, i.e., within the j-th subimage, and

, затемget the middle phase

then

, далее,the phases of the spatial spectra of the image fragments belonging to different subimages are averaged, that is, averaged over j and the average phase is obtained

, Further,

, а также, учитывая статистическую однородность объекта, при которой

,taking into account that the average atmospheric phase of the OPF of the atmosphere-telescope system is identically equal to zero

, and also, given the statistical homogeneity of the object, at which

,

, среднюю фазу пространственного спектра фрагментов изображения, усредненную по j

, иsubtract from the middle phase of the spatial spectrum of the image fragments, averaged over i,

, the average phase of the spatial spectrum of image fragments averaged over j

, and

, затемget the phase of the instantaneous OPF of the atmosphere-telescope system for the j-th subimage

then

и фазе

формируют мгновенную ОПФ системы атмосфера-телескоп для j-того субизображения в виде

, и,according to the received module

and phase

form an instantaneous OPF of the atmosphere-telescope system for the j-th subimage in the form

, and,

using it for inverse filtering of the spatial spectrum of the j-th subimage,

,receive an undistorted atmosphere spatial spectrum of the j-th area of the isoplanarity of the object

,

,with the inverse Fourier transform, from which the diffraction-limited subimage of the j-th isoplanatic section of the object is restored, which is undistorted by the atmosphere

,

performing the same processing for the remaining (N-1) sub-images of the recorded remote sensing image, restore N-1 diffraction-limited isoplanatic sub-images of the object,

combine them in one frame with each other and with the previously restored j-th subimage, given their location and orientation in the recorded image,

.and restore the undistorted atmosphere diffraction-limited image of the object (an extended section of the probed earth's surface)

.

The essence of the claimed invention is illustrated in the following description.

In FIG. 1 presents a variant of the scheme of practical implementation of the proposed method, which shows the following:

in FIG. 1a is a structural diagram of a remote sensing imaging channel, in which:

1 - wide-angle telescope of a remote sensing spacecraft;

2 - collimating optics;

3 - turret with narrow-band interference light filters (Δλ≤Δλ _A = 250 A ⁰ );

4 - focusing optics;

5 - focal plane of the image;

in FIG. 1b is a structural diagram of a channel for detecting and recording remote sensing images, in which:

5 - focal plane of the image;

6 - electromechanical shutter;

7 - image brightness amplifier;

8 - image transfer optics;

9 - quadratic panoramic detector;

10 - digital video processing system;

11 - on-board computer;

12 - encoding device;

13 - airborne radar station (radar);

in FIG. 1c is a block diagram of a remote sensing image processing channel, in which:

14 - ground radar;

15 - decoding device;

16 - computing means;

17 - software;

18 - algorithmic support for the processing of remote sensing images;

19 - operator workstation;

20 - consumers of high resolution remote sensing images.

It should be noted that the remote sensing imaging channel and the remote sensing image detection and registration channel are located onboard the remote sensing spacecraft, and the remote sensing image processing channel is located on Earth and is connected to them via a radio link.

The operation of the remote sensing system as shown in FIG. 1 structural diagrams as follows.

и полосу принимаемого светового излучения Δλ, причем здесь при спектральной фильтрации Δλ≤Δλ_А, а

, где σ_θ - среднеквадратичное отклонение атмосферных искажений фазы θ_А светового излучения. Выполнение условия Δλ≤Δλ_А обеспечивает отсутствие частотного усреднения атмосферных искажений фазы волнового фронта светового излучения в изображении ДЗЗ, формируемом фокусирующей оптикой 4.The wide-angle telescope of the DZZ 1 spacecraft carries out the formation of an optical image of an extended portion of the probed earth's surface, observed from space through a turbulent atmosphere. The collimating optics 2 creates a parallel beam of light necessary for the correct operation of subsequent optical elements. Turret with interference filters 3, each of which with the solar illumination of the probed area of the earth's surface allows you to select the necessary spectral range

and the band of received light radiation Δλ, and here with spectral filtering Δλ≤Δλ _A , and

where σ _θ is the standard deviation of atmospheric distortions of the phase θ _{A of} light radiation. The fulfillment of the condition Δλ≤Δλ _A ensures the absence of frequency averaging of atmospheric distortions of the phase of the wave front of the light radiation in the remote sensing image formed by the focusing optics 4.

Focusing optics 4 forms a filtered image of the object in the focal plane 5, containing the shutter 6 of the channel for detecting and recording images. Electromechanical gate 6 is synchronized with the frame rate of a quadratic and a panoramic detector 9 provides the required exposure time of short-exposure images τ _E to obtain instantaneous short-exposure image. The brightness amplifier of the image 7 compensates for the attenuation of the received light radiation during spectral filtering of 3 and provides the noise-optimal operation of the quadratic panoramic detector 9 with quantum noise prevailing over other noise of the detection process [1]. It is advisable to use a microchannel plate (MCP), which has less weight and dimensions than an electron-optical converter (EOC), as an amplifier for the brightness of image 7 on board an ERS spacecraft.

The transfer optics 8 projects the image of the object from the output of the image intensifier 7 to the input of a quadratic panoramic detector 9 without changing the angle. As the transfer optics, you can use, for example, a set of lenses or fiber optics with less light loss during image transmission. Quadratic panoramic detector 9 is designed to detect spectrally filtered short-exposure images. It is advisable to use a matrix based on charge-coupled device technology (CCD matrix) as a quadratic panoramic detector on board an ERS spacecraft, which has less weight and dimensions than a super-siliconnik TV detector.

The digital video processing system 10 is designed to digitize a short-exposure remote sensing image from a quadratic panoramic detector 9. The 10-digit video signals from a quadratic panoramic detector 9 are recorded in the digital memory of the on-board computer 11. Next, the digitized short-exposure image from the computer 11 encoding device 12 and using radar 13 on a radio line is transmitted to the Earth for further processing. Processing of a spectrally filtered short-exposure image of the probed portion of the earth’s surface obtained on board an ERS spacecraft in accordance with FIG. 1a and FIG. 1b and transmitted over the air to the Earth, carried out according to the scheme shown in FIG. 1c.

The ground-based radar 14 receives information from the airborne radar 13 via a radio link. The decoding device 15 converts the signals from the ground-based radar 14 to a form convenient for recording in the memory of ground-based computing tools 16. Computing tools 16 are designed to implement an image processing algorithm for remote sensing images 18. Software 17 computing means 16 is intended to organize the process of their work and implement the remote sensing image processing algorithm 18. The algorithmic support 18 of remote sensing image processing proposed in this application for The invention provides a sequence of operations on a registered spectrally-filtered short-exposure remote sensing image that is spatially non-invariant to atmospheric distortions, ensuring the achievement of the goal of reconstructing an undistorted image of an object that has diffractive resolution of the remote sensing telescope in its wide field of view. The operator’s AWP 19 is designed to control the process of processing and analyzing the spatial resolution of the processed image during the implementation of the image processing algorithm 18. After processing, the reconstructed image of the remote sensing remote sensing of ultra-high (diffraction) resolution is transmitted to consumers 20.

We give a brief mathematical justification of the proposed method in terms of algorithmic support 18 for digital processing of the registered image.

When remotely sensing the Earth's surface illuminated by the Sun, the intensity distribution of the recorded spectrally-filtered (Δλ≤Δλ _A ) short-exposure (τ _E ≤ τ _A ) image of an object (an extended non-planar part of the earth's surface), neglecting additive noise, can be represented as an integral of a superposition of the form

- истинное распределение интенсивности объекта,

- мгновенный импульсный отклик системы атмосфера-телескоп ДЗЗ (функция рассеяния точки).Where

- the true distribution of the intensity of the object,

- instantaneous impulse response of the atmosphere-telescope remote sensing system (dot scattering function).

является различной для разных точек

объекта

что не позволяет применить теорему свертки теории Фурье преобразований к выражению (1) и получить соответствующее его описание в пространственно-частотной области.Due to the spatial non-invariance of the recorded image (1), the function

is different for different points

facility

which does not allow us to apply the convolution theorem of the Fourier theory of transformations to expression (1) and obtain its corresponding description in the space-frequency domain.

To perform spatial filtering of the obtained non-planar image, it is divided into N subimages comparable with the size of the isoplanatic region of the atmosphere-telescope remote sensing system, i.e., into N regions, within each of which the system is spatially invariant.

Then, for each jth subimage, expression (1) can be represented by a convolution integral of the form

where j = 1, 2 ..., N is the index indicating the number of the j-th subimage and atmospheric realization, which took part in the formation of the j-th subimage.

Now, in the presence of spatial invariance of each subimage, transforming both sides of equation (2) according to Fourier, we obtain its description in the space-frequency domain in the form

- модуль пространственно-частотного спектра искаженного j-того субизображения;

- модуль пространственного спектра истинного j-того субизображения объекта и модуль ОПФ (оптической передаточной функции) системы атмосфера-телескоп ДЗЗ для j-того участка изопланатичности, а

,

,

- фазы соответствующих спектров и ОПФ системы атмосфера-телескоп ДЗЗ.Here

- the module of the spatial frequency spectrum of the distorted j-th sub-image;

- the spatial spectrum module of the true j-th subimage of the object and the OPF module (optical transfer function) of the atmosphere-telescope remote sensing system for the j-th isoplanatic section, and

,

,

- phases of the corresponding spectra and the OPF of the atmosphere-telescope ERS system.

Next, each sub-image is divided into M fragments corresponding to the number of resolution elements of the atmosphere-telescope system within the isoplanatic region.

By analogy with (2) and (3), we can write the expression for the ith fragment of the jth subimage in the form

and its spatial spectrum in the form

и

- модуль и фаза пространственного спектра ij-того фрагмента истинного распределения интенсивности объекта, а звездочка * обозначает операцию свертки, аналогичную (2).Here i = 1, 2 ..., M is the index indicating the number of the sub-image fragment, and M is their number in the isoplanatic region (sub-image),

and

is the modulus and phase of the spatial spectrum of the ijth fragment of the true distribution of the intensity of the object, and the asterisk * denotes a convolution operation similar to (2).

Further, in accordance with the proposed method, the processing of phase and amplitude information in the spatial spectrum is carried out separately.

The square of the spatial spectrum modulus of each ij image fragment is defined as:

We average this value over index i, i.e., we find the average square modulus of the spatial spectrum of each image fragment within the jth subimage

обозначает операцию усреднения.Where

denotes the averaging operation.

Now averaging (6) over the index j, i.e., averaging the fragments over N subimages

представляет собой средний квадрат модуля ОПФ системы атмосфера-телескоп, которая в общем случае является аналитически известной для данных условий наблюдения [12] (Korff D. «Analysis of a method for obtaining near-diffraction-limited information in the presence of atmospheric turbulence», JOSA,v. 63, p. 971, 1973) и с учетом принципа «взаимности» распространения [1] определяется соотношениемHere is the function

represents the average square of the OPF module of the atmosphere-telescope system, which is generally analytically known for these observation conditions [12] (Korff D. “Analysis of a method for obtaining near-diffraction-limited information in the presence of atmospheric turbulence”, JOSA, v. 63, p. 971, 1973) and taking into account the principle of “reciprocity” of distribution [1] is determined by the relation

- пространственно-частотный вектор в апертуре

телескопа ДЗЗ,

,

- радиусы-векторы положения (координат), соответственно, точек 1 и 2 плоскости апертуры

телескопа ДЗЗ,

- средняя длина волны солнечного излучения подсвета

, F - фокусное расстояние телескопа ДЗЗ,

- оптическая передаточная функция (ОПФ) телескопа ДЗЗ, определяемая для круглой апертуры телескопа диаметра D соотношениемWhere

- spatial frequency vector in the aperture

remote sensing telescope,

,

- the radius vectors of the position (coordinates), respectively, of points 1 and 2 of the aperture plane

remote sensing telescope,

- the average wavelength of solar radiation backlight

, F is the focal length of the remote sensing telescope,

- optical transfer function (OPF) of the remote sensing telescope, determined for the circular aperture of a telescope of diameter D by the ratio

- пространственный радиус корреляции атмосферных флуктуаций светового излучения, отраженного от земной поверхности, на высоте Н космического аппарата ДЗЗ, определяемый [5], какbut

- the spatial radius of the correlation of atmospheric fluctuations of light radiation reflected from the earth's surface, at a height H of the remote sensing spacecraft, defined [5] as

- величина пространственного радиуса корреляции атмосферных флуктуаций светового излучения на границе турбулентного слоя L (L≈10 км).Where

- the value of the spatial radius of the correlation of atmospheric fluctuations of light radiation at the boundary of the turbulent layer L (L≈10 km).

, определяемый (9), для инверсной фильтрации

, определяемого (8), получаем средний квадрат модуля пространственного спектра фрагментов объекта

Using further

defined by (9) for inverse filtering

defined by (8), we obtain the mean square modulus of the spatial spectrum of the object fragments

Most real extended remote sensing objects are statistically uniform, that is, for them the equality

в (7), в результате инверсной фильтрации получаем квадрат модуля мгновенной ОПФ системы атмосфера-телескоп для j-того субизображенияSubstituting the value obtained taking into account (12) and (13)

in (7), as a result of inverse filtering, we obtain the square of the modulus of the instantaneous OPF of the atmosphere-telescope system for the jth subimage

extracting the square root from which, we obtain the modulus of the instantaneous OPF of the atmosphere-telescope system for the j-th subimage (j-th region of isoplanarity of the recorded image)

Simultaneously with the restoration of the instantaneous OPF module, its phase is restored. It is easy to see from (5) that

To obtain the phase of the instantaneous OPF of the atmosphere-telescope system for the j-th isoplanatic region, first phase (16) is averaged over i, i.e., for fragments belonging to one subimage, then

усредняют (16) по j, то есть усредняют фазы пространственных спектров фрагментов, относящихся к разным субизображениямThen, in order to eliminate in (17) the middle phase of the spatial spectrum of the object

averaging (16) over j, i.e., averaging the phases of the spatial spectra of fragments belonging to different subimages

(Бакут П.А., Свиридов К.Н., Устинов Н.Д. О возможности восстановления неискаженного атмосферой изображения объекта по N его пятенным интерферограммам. Оптика и спектроскопия, т. 50, вып. 6, с. 1191, 1981), с учетом статистической однородности объекта ДЗЗGiven that

(Bakut P.A., Sviridov K.N., Ustinov N.D. On the possibility of restoring an undistorted image of an object from N by its spot interferograms. Optics and Spectroscopy, vol. 50, issue 6, p. 1191, 1981), taking into account the statistical homogeneity of the remote sensing object

Subtract (18) from (17) and obtain the phase of the instantaneous OPF for the jth subimage

So, having restored the module (15) and phase (20) of the instantaneous OPF of the atmosphere-telescope system for the jth subimage, form its instantaneous OPF in the form

Carrying out further inverse filtering of the spatial spectrum of the jth subimage (3) of the generated OPF (21), one obtains a diffraction limited spatial spectrum of the jth filtered subimage of the object

and with the inverse Fourier transform, the diffraction-limited subimage of the jth isoplanatic portion of the earth's surface is undistorted by the atmosphere from it

Performing a processing similar to that described above for the remaining (N-1) isoplanatic regions of the registered spectrally-filtered short-exposure image (1), (N-1) subimages of the form (23) are restored, they are combined in a single frame with each other and with previously restored j- a subimage, taking into account their location and orientation in the recorded image, and restore the undistorted atmosphere diffraction-limited image of the object (an extended portion of the probed earth's surface) I ₀ .

Consider the practical implementation of the proposed method for obtaining and processing remote sensing images distorted by a turbulent atmosphere, according to the scheme shown in FIG. one.

To obtain a spectrally filtered short-exposure image of an object that is spatially non-invariant to atmospheric distortions, it is necessary to have a wide-angle telescope 1 on the remote sensing spacecraft. In this case, the instantaneous image of the remote sensing object, obtained in a wide field of view, will consist of N instantaneous isoplanarity regions of the atmosphere system telescope remote sensing. As a wide-angle mirror reflector telescope with a ring aperture, it is necessary to use, for example, the Ricci-Chretien aplanatic system with a main hyperbolic mirror, which provides a much larger field of view compared to traditional parabolic mirror telescopes. In the direct focus of a large Ritchie-Chretien telescope, using three lens corrector, it is possible to provide a field of view with a diameter> 1 ° [14] (P. Scheglov, Problems of Optical Astronomy. Moscow: Nauka, 1980).

. Согласно экспериментальных данных величина σ_θ может изменяться в широких пределах и имеет значения порядка (10÷20) рад., что для

(

мкм) дает величину Δλ_А=(500÷250)А⁰, откуда Δλ≤250 А⁰.When receiving an instant (short-exposure) image of an object, to eliminate the frequency averaging of atmospheric distortions in the generated image, it is necessary to carry out spectral filtering of the received light radiation. According to previous studies [15] (Sviridov K.N. et al. Static Evaluation of the Spectral Band of the Spot Interferometry Method. Optics and Spectroscopy, vol. 54, issue 5, p. 890, 1983) the frequency band Δλ, turrets with interference filters 3 is selected based on the standard deviation σ _{θ of} atmospheric distortions of the phase θ _{A of} light radiation and is determined by the ratio

. According to experimental data, the value of σ _θ can vary over a wide range and has values of the order of (10–20) rad., Which for

(

μm) gives the value Δλ _A = (500 ÷ 250) A ⁰ , whence Δλ≤250 A ⁰ .

The required spectral filtering band turns out to be rather narrow and noticeably weakens the brightness of the formed image. To compensate for this attenuation, the brightness of the image formed in the image intensifier is amplified before detection 7. For detection of a short-exposure remote sensing image in a quadratic panoramic detector 9, the exposure time (registration) τ _E should be less than the time of “frozen” atmospheric turbulence τ _A. In accordance with the experimental data, the value of _A varies over a wide range of τ _A = (1 ÷ 100) ms, and has a minimum value of τ _Amin = 1 ms. Given this, when short-exposure registration of the remote sensing image is necessary, the shutter 6 must provide τ _E ≤τ _A = 1 ms.

, для достижения упомянутого выше поле зрения телескопа 1° при фокусном расстоянии телескопа F=10 м, размер рабочего поля приемника должен быть равен D_пз = 0,0175 рад. × 10 м = 17,5 см. Такое рабочее поле приемника изображения - 9 является практически достижимым, например, путем комбинирования нескольких диодных матриц меньшего размера. Далее оцифрованное в цифровой системе обработки видеосигналов 10 и зарегистрированное в цифровой памяти бортового компьютера 11 изображение ДЗЗ кодируется в 12 и с помощью 13 по радиолинии передается на Землю для последующей обработки.As a quadratic panoramic detector 9, it is necessary to use a solid-state electronic detector of the CCD type based on photoconductivity. Solid-state diode arrays with electronic scanning of a raster have advantages both in comparison with a photodetector and in comparison with a TV vacuum electronic detector [1], and are in good agreement with the MCP image amplifier 7. For detecting and recording a remote sensing image in a wide field of view of the telescope, a quadratic panoramic receiver (detector) 9 should have a wide working field of diameter D _p. Given that the field of view of the telescope-receiver system is determined by the ratio [1]

, to achieve the aforementioned field of view of the telescope 1 ° at a focal length of the telescope F = 10 m, the size of the working field of the receiver must be equal to D _PZ = 0,0175 rad. × 10 m = 17.5 cm. Such a working field of the image receiver - 9 is practically achievable, for example, by combining several smaller diode arrays. Further, the remote sensing image digitized in the digital video signal processing system 10 and recorded in the digital memory of the on-board computer 11 is encoded in 12 and transmitted via the radio link to the Earth using the radio link 13 for further processing.

In accordance with the proposed method for implementing algorithm 18 when processing a registered spectrally-filtered short-exposure remote sensing image that is spatially non-invariant to atmospheric distortions, the following sequence of operations is presented, shown in FIG. 2:

системы атмосфера-телескоп ДЗЗ в фокальной плоскости

изображения 5 широкоугольного телескопа 1, как1) for given Earth observation conditions, the size of the instantaneous isoplanatic region is determined

focal plane atmosphere-telescope remote sensing systems

image 5 of wide-angle telescope 1 as

и F определены выше,where the values are:

and F are defined above,

размера

;and form a "sliding window" in the form of a U-shaped function

the size

;

;2) using the “sliding window” formed in step 1), the remote sensing image [formula (1)] N sub-images [formula (2)] are commensurate with the size of the instantaneous isoplanarity of the atmosphere-telescope system

;

, как3) for the given observation conditions, determine the size of the resolution element of the atmosphere-telescope remote sensing system in the focal plane of the image

, as

определено в формуле (11), и, используя аналогичное операции 2) «скользящее окно» в виде П-образной функции размера

выделяют в каждом j-том субизображении (2) М фрагментов (4), соизмеримых с элементом разрешения системы атмосфера-телескоп ДЗЗ -

;Where

defined in formula (11), and using a similar operation 2) a “sliding window” in the form of a U-shaped size function

in each j-th subimage (2) M fragments (4) are selected that are comparable with the resolution element of the atmosphere-telescope remote sensing system -

;

4) transform each j-th subimage (2), spatially invariant to atmospheric distortions, according to Fourier into the region of its spatial spectrum

пространственно-частотный вектор в апертуре

телескопа ДЗЗ, j=1, 2, … N,Where

spatial frequency vector in the aperture

Remote sensing telescope, j = 1, 2, ... N,

and get the spatial spectrum of each j-th subimage (26) in the form of expression (3);

5) similarly transform each ij-th fragment (4) according to Fourier into the region of its spatial spectrum

where i = 1, 2, ... M; j = 1, 2, ... N,

and get the spatial spectrum of each image fragment (27) in the form of expression (5).

Further, in accordance with the proposed method, the processing of the amplitude and phase information of the spatial sectors of the image fragments (5) is carried out separately;

пространственных спектров фрагментов изображения (5) в соответствии с выражением (6);6) allocate squares of modules

spatial spectra of image fragments (5) in accordance with expression (6);

по индексу i, то есть формируют величину

и получают средний квадрат модуля пространственного спектра фрагментов изображения в пределах j-того субизображения

в соответствии с выражением (7);7) average the value

by index i, that is, form the value

and get the average square modulus of the spatial spectrum of the image fragments within the j-th subimage

in accordance with the expression (7);

по индексу j, то есть формируют величину

и получают средний квадрат модуля пространственного спектра фрагментов изображения по N субизображениям

в соответствии с выражением (8);8) then average the value

by index j, that is, form the value

and get the average square modulus of the spatial spectrum of the image fragments from N sub-images

in accordance with the expression (8);

, определяемый для данных условий наблюдения соотношением (9);9) form the average square of the OPF module of the atmosphere-telescope system

determined for these observation conditions by the relation (9);

, определяемого выражением (8), сформированным средним квадратом модуля ОПФ системы атмосфера-телескоп (9) и получают средний квадрат модуля пространственного спектра фрагментов объекта, усредненного по N субизображениям,

в соответствии с выражением (12);10) carry out inverse filtering of the average square of the module of the spatial spectrum of image fragments averaged over N subimages

defined by the expression (8) formed by the average square of the module of the OPF of the atmosphere-telescope system (9) and get the average square of the module of the spatial spectrum of fragments of the object averaged over N subimages,

in accordance with the expression (12);

к среднему квадрату модуля пространственного спектра фрагментов объекта, усредненному по М фрагментам в пределах одного субизображения,

в соответствии с выражением (13);11) taking into account the statistical homogeneity of the object, equate the average square modulus of the spatial spectrum of the fragments of the object, averaged over N subimages,

to the average square of the module of the spatial spectrum of the object fragments, averaged over M fragments within the same subimage,

in accordance with the expression (13);

, полученного в операции 7) в соответствии с выражением (7), средним квадратом модуля пространственного спектра фрагментов объекта, получаемым в операции 11) в соответствии с выражением (13), и получают при этом квадрат модуля мгновенной ОПФ системы атмосфера-телескоп ДЗЗ для j-того субизображения

в соответствии с (14);12) taking into account formulas (12) and (13), inverse filtering of the average square of the module of the spatial spectrum of image fragments is carried out

obtained in operation 7) in accordance with expression (7), the average square of the modulus of the spatial spectrum of the object fragments obtained in operation 11) in accordance with expression (13), and the square of the module of the instantaneous OPF of the atmosphere-telescope remote sensing system for j sub image

in accordance with (14);

и получают модуль мгновенной ОПФ системы атмосфера-телескоп для j-того субизображения в соответствии с выражением (15);13) remove the square root of

and get the module instantaneous OPF atmosphere-telescope system for the j-th subimage in accordance with the expression (15);

вида (16);14) simultaneously with the restoration of the instantaneous OPF module for the j-th sub-image, its phase is restored, for which the phases of the spatial spectra of image fragments are isolated in formula (5)

type (16);

(16) сначала по i, то есть по фрагментам одного j-того субизображения и получают среднюю фазу

в соответствии с выражением (17);15) average phases

(16) first, by i, i.e., by fragments of one j-th subimage, and obtain the middle phase

in accordance with the expression (17);

(16) по j, то есть, усредняют фазы пространственный спектров фрагментов изображения, относящихся к разным субизображениям, и получают

в соответствии с выражением (18);16) then average the phases

(16) over j, that is, the phases of the spatial spectra of the image fragments belonging to different subimages are averaged and obtained

in accordance with the expression (18);

, а так же, статистическую однородность объекта ДЗЗ в соответствии с (19), вычитают (18) из (17) и получают фазу мгновенной ОПФ для j-того субизображения

в соответствии с выражением (20);17) considering in (18) that

, as well as the statistical homogeneity of the remote sensing object in accordance with (19), subtract (18) from (17) and obtain the phase of the instantaneous OPF for the jth subimage

in accordance with the expression (20);

в виде выражения (21);18) restoring the module (15) in operation 13), and in the operation 17) the phase (20) of the instantaneous OPF of the atmosphere-telescope system for the jth subimage, form its instantaneous OPF

in the form of expression (21);

(3), полученного в операции 2), мгновенной ОПФ (21), сформированной в операции 18), и получают при этом дифракционно-ограниченный пространственный спектр j-того отфильтрованного изображения объекта

, определяемого выражением (22);19) inverse filter the spatial spectrum of the jth subimage

(3) obtained in operation 2), instantaneous OPF (21), formed in operation 18), and in this case, a diffraction-limited spatial spectrum of the jth filtered image of the object is obtained

defined by the expression (22);

(22), полученного в операции 19), и восстанавливают при этом неискаженное атмосферой дифракционно-ограниченное телескопом ДЗЗ изображение j-того изопланатичного участка зондируемой земной поверхности

в соответствии с формулой (23);20) carry out the inverse (26) Fourier transform of

(22) obtained in operation 19), and the image of the jth isoplanatic portion of the probed earth's surface, diffraction-limited by the remote sensing telescope, is reconstructed with an undistorted atmosphere

in accordance with formula (23);

21) simultaneously carry out the same processing performed in accordance with operations 3) ÷ 20) for the remaining (N-1) subimages (2) obtained in operation 2), and restore (N-1) diffraction-limited subimages of the form (23);

.22) taking into account the previously used in 2) U-shaped function of the “sliding window”, all N reconstructed in operations 20) and 21) subimages are combined in one frame for all the isoplanarity regions selected in operation 2) taking into account their location and orientation in the original recorded image of the object (1) and restore at the same time the undistorted atmosphere diffraction-limited image of the object (an extended section of the probed earth's surface)

.

Implementation of the proposed method allows to simplify and speed up the process of obtaining images, since here, unlike the prototype, it is not necessary to obtain a series of N images of an object that are independent of each other by atmospheric distortions, and only one spectrally filtered short-wavelength is recorded in a wide field of view exposure image of the object, spatially non-invariant to atmospheric distortions. During its subsequent digital processing, atmospheric distortions are compensated and the image of the object is restored with a resolution determined by the diffraction resolution of the remote sensing telescope in its wide field of view.

It is easy to verify that, in comparison with the prototype, the proposed method allows to accelerate the process of obtaining images and provides a temporary gain equal to T _B = (N-1) (τ _E + τ _P ) sec, where τ _P is the time interval between the images introduced in the prototype series independent of atmospheric distortion. Then, with N = 10 ³ , τ _E = 1 ms and τ _P = 140 ms, the time gain in obtaining images of the proposed method compared to the prototype is T _B = 141 sec = 2.35 min, which is a significant technical result when taking into account the speed of movement remote sensing spacecraft.

.Another important technical result of the proposed method in comparison with the prototype and analogues is the compensation of atmospheric distortions in it and the achievement of diffraction resolution of the image restored during processing in a wide field of view. So, if in the prototype the resolution of the reconstructed image was determined by the average short-exposure OPF of the atmosphere-telescope system, then in the proposed method the resolution of the reconstructed image is determined by the OPF of the telescope. Depending on the diameter D of the receiving aperture of the remote sensing telescope and the height H of the remote sensing aerospace vehicle above the earth's surface, the resolution gain of the proposed method can be from 10 to 15 times at

.

Information sources

1. Sviridov K.N. Technologies for achieving high angular resolution of optical atmospheric vision systems. M .: Knowledge, 2005.

2. Petri G. Russian satellite “Resource-DK1”: an alternative source of ultra-high resolution data. Geomatics, No. 4, p. 38-42, 2010.

3. Kirilin A.N. and others. Resurs-P spacecraft. Geomatics, No. 4, p. 23-26, 2010.

4. Lavrov V.V. Ultra-high-resolution space survey systems. Geoinformation portal of the GIS Association, No. 2, 2010.

5. Sviridov K.N. On the limiting resolution of aerospace systems for remote sensing of the Earth (ERS). Magazine "Rocket and Space Instrument Engineering and Information Systems", vol. 1, no. 1, p. 34, 2014.

6. Sviridov K.N., Volkov S.A. Earth remote sensing method. Application for invention No. 2015129353 dated 07/17/2014, the applicant is JSC “Russian Space Systems”.

7. Sviridov K.N. Remote sensing of the Earth with adaptive compensation for random wavefront tilts. The journal “Rocket and Space Instrument Engineering and Information Systems”, vol. 2, no. 3, p. 12, 2015.

8. Sviridov K.N. A method of obtaining and processing images distorted by a turbulent atmosphere. The application for the invention RU 2016100934 from 01/14/2016, the applicant JSC "Russian Space Systems".

9. Sviridov K.N. Adaptive filtering of medium images distorted by a turbulent atmosphere. The journal “Rocket and Space Instrument Engineering and Information Systems”, vol. 2, no. 4, p. 40, 2015.

10. Sviridov K.N. The method of remote sensing of the Earth (ERS). Patent for invention RU 2531024 dated 08/20/2014 according to the application RU 2013125540 dated 06/03/2013, the applicant and patent holder of JSC Russian Space Systems.

11. Sviridov K.N. About a new approach to obtaining and processing remote sensing images distorted by a turbulent atmosphere. Magazine "Rocket and Space Instrument Engineering and Information Systems", vol. 1, no. 4, p. 28, 2014.

12. Korff D. Analysis of a method for obtaining near-diffraction-limited information in the presence of atmospheric turbulence, JOSA, v. 63, p. 971, 1973.

13. Bakut P.A., Sviridov K.H., Ustinov H.D. On the possibility of restoring an object's undistorted image of an object from N of its spot interferograms. Optics and Spectroscopy, vol. 50, no. 6, p. 1191, 1981.

14. Scheglov P.V. Problems of optical astronomy. M .: Nauka, 1980.

15. Sviridov K.N. et al. Static estimation of the spectral band of the spot interferometry method. Optics and Spectroscopy, vol. 54, no. 5, p. 890, 1983.

Claims (39)

The method of obtaining and processing images of remote sensing of the Earth, distorted by a turbulent atmosphere, which consists in the fact that on board the Earth’s remote sensing spacecraft receive in a wide field of view the Earth’s remote sensing telescope a spectrally filtered short-exposure image of object I _and (l) - an extended portion of the probed earth's surface, spatially non-invariant to atmospheric distortions, and transmit it to the Earth for digital processing, in which the size of the instantaneous isoplanarity region of the atmosphere-telescope system of remote sensing of the Earth in the recorded image is first determined

and allocate N sub-images in it

commensurate with the size of the isoplanatic region, and in each j-th subimage M fragments are distinguished

commensurate with the resolution element of the atmosphere-telescope system of remote sensing of the Earth

then transform every j-th subimage

and every ij-th fragment

according to Fourier to the region of their spatial spectra

and

where highlight the squares of the modules

and phases

obtained MN spatial spectra

and at the same time carry out their separate statistical processing, for which first, the squares of the spatial spectrum moduli M of the image fragments are averaged over i and get the average square of the spatial spectrum modulus of the image fragments within the j-th subimage

and then similarly average the squares of the moduli of the spatial spectra of N image fragments over j and get the average square of the spatial spectrum modulus of the image fragments from N subimages

, Further form the average square of the optical transfer function module of the atmosphere-telescope system of remote sensing of the Earth

being analytically known for given observation conditions, and using it for inverse filtering of the average square of the modulus of the spatial spectrum of image fragments averaged over N subimages

, get the average square modulus of the spatial spectrum of the fragments of the object, averaged over N subimages

, Further considering the statistical homogeneity of the Earth's remote sensing object, equate the average square modulus of the spatial spectrum of fragments of an object averaged over N sub-images

to the average square of the modulus of the spatial spectrum of the object fragments averaged over M fragments of the j-th subimage

and use it

for inverse filtering of the mean square modulus of the spatial spectrum of image fragments averaged over i within the jth subimage

, while restoring the square of the modulus of the instantaneous optical transfer function of the atmosphere-telescope system of remote sensing of the Earth for the jth subimage

, but, extracting the square root from it, get the module of the instantaneous optical transfer function of the atmosphere-telescope system of remote sensing of the Earth for the j-th subimage

, simultaneously for recovering the phase of the instantaneous optical transfer function of the j-th subimage

first phase phase spatial spectra of image fragments are averaged

by i, i.e., within the j-th subimage, and get the middle phase

, and then averaging the phases of the spatial spectra of the image fragments related to different subimages, i.e. average

by j and get the middle phase

, Further taking into account that the average of atmospheric fluctuations of the phase of the optical transfer function of the atmosphere-telescope system of remote sensing of the Earth is identically equal to zero

, as well as given the statistical homogeneity of the Earth's remote sensing object, at which

, subtracted from the middle phase of the spatial spectrum of the image fragments, averaged over

, the middle phase of the spatial spectrum of image fragments averaged over

, and get the phase of the instantaneous optical transfer function of the atmosphere-telescope system of remote sensing of the Earth for the j-th subimage

then according to the received module

and phase

form the instantaneous optical transfer function of the atmosphere-telescope system of remote sensing of the Earth for the j-th subimage

, and using it for inverse filtering of the spatial spectrum of the j-th subimage

, receive an undistorted atmosphere spatial spectrum of the j-th area of the isoplanarity of the object

, with the inverse Fourier transform from which the diffraction-limited subimage of the j-th isoplanatic section of the object is restored, which is undistorted by the atmosphere

, performing the same processing of the remaining N-1 sub-images of the recorded image of Earth remote sensing, restore the N-1 diffraction-limited isoplanatic sections of the object, combine them in one frame with each other and with the previously restored j-th sub-image, given their location and orientation in the recorded image, and restore the atmosphere-undistorted diffraction-limited image of the Earth remote sensing object - an extended non-isoplastic portion of the probed Earth's surface

.

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