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Image velocimetry of atmospheric inhomogeneities using a statistical approach
Optics Communications90 (1992) 16-20 North-Holland
OPTICS COM MUNICATIONS
Image velocimetry of atmospheric inhomogeneities using a statistical approach V.A. M i t e v a n d G.I. Sokolinov Bulgarian Academy of Sciences, Institute of Electronics, Sofia 1784, Bulgaria Received 10 July 1991; revised manuscript received 16 December 1991
Velocity measurements of imaged cloud fields have been conducted by gathering time-spatial realizations. Properly selected data are used to produce at least three dependencies of temporary instabilities for moving dots in the imaged area. The modulus and the direction of the velocityvector are determined after fixingthe coordinates of the minimum value for every gained dependence. Two algorithms for data acquisition and processing have been developed. Consecutive measurementsfor cloud velocity determination have been carried out in three-minute periods.
1. Introduction
The registration and processing of image sequences is applied with an increasing rate in the remote sensing and control for measuring the velocity and estimating the motion of different objects. The main advantage of this technique is in the possibility for express analysis of large spatial areas with a high information gain. The double-exposure photography methods are often used to obtain the velocity of objects, including air flows [ 1 ]. If one investigates a seeded flow movement, depending on the panicle dimensions and concentration, the velocity measurements are accomplished by processing specklegrams or by tracing out different particles on the registered images. The optical methods for speckle-pattern processing are based on the two-dimensional Fourier transformation. It is applied to tiny separate areas of the image to produce interference patterns, which contain information about the movement of the object [ 1-3 ]. The processing of the interference patterns, as well as the direct determination of the velocity vectors by registration of images [ 4-7 ] could be carried out using different digital methods. The velocity vector could be also obtained without producing interferograms optically [4 ]. After digitizing the registered images and adding their relevant pixel intensities, the information is analyzed by applying a digital Fourier 16
transformation. Digital filtering was used to demonstrate selection of particles moving with equal velocities [ 5 ]. An algorithm, built on the basis of crosscorrelation between two successively captured images was also used for obtaining the velocity by estimating the drift of particle clumps [ 6 ]. A similar correlation method, used as a basis for designing an imaging system for passive remote sensing of cloud fields has been described earlier [ 7], However, the imaged field is treated as a moving object, where individual particles or clumps are not considered. The main drift velocity vector is set by the position of the global correlation maximum, which is obtained for different couples of registered images. Using an image receiver for the implementation of the method also provides the measurement of moment velocity values. Correlation remote sensing methods give an opportunity to measure both the main drift velocity of aerosol inhomogeneities and their statistical features (life time, space scales and orientation) as well [ 8,9 ]. The following obstacles oppose this universality: huge quantity data processing, the necessity for many sophisticated computing operations, strong accuracy dependence of the result on the statistical inhomogeneity and instability of the aerosol field. The speed of data handling and the measurement rate could be considerably increased by a kind of simplified statistical information processing, which
0030-4018/92/$ 05.00 © 1992 Elsevier Science Publishers B.V. All fights reserved.
Volume 90, number 1,2,3
OPTICS COMMUNICATIONS
however provides determination only of the velocity [ 10 ]. Developing this idea, we have put into practice a method for remote measurement of the velocity by capturing time-spatial realizations of the investigated aerosol field, using an image array receiver, and by building the temporary instabilities of these realizations.
2. A brief method description The idea of the method has been described in detail earlier in ref. [ 10]. Following is a summary of the main points. (i) In the plane of the receiver three coordinate systems are introduced: one fixed relative to the imaging camera (Xo, Yo), one moving with the real velocity of the aerosol inhomogeneities (x~, Yv) and another (x,, y,) moving with a variable preset velocity. K images of the investigated field are registered in different moments &, ( x = 1, 2, ..., k) using successive constant-time exposures, separated by equal time periods. All the images collected in one measurement cycle form a time-spatial realization ot = ¢o (Xo, Yo, t), which consists of the image-data developed in time. (ii) The time-spatial realization a=q~o(Xo, Yo, t) is interpreted as time-dependent only (t) realizations of clots in the image field moving with velocities U, in the plane (Xo, Yo) and motionless in the coordinate system (x,, y,). These t-realizations are achieved after suitable selection of the data from every frame in three preselected directions (line x, column y and the diagonal d of the image receiver), so that three matrices are constructed. Their dimensions are fixed by the number of pixels in the relevant direction and by the number of exposures, used to form one time-spatial realization. The directions chosen could also be arbitrarily selected as long as they are not permitted to be parallel. The essential idea is that appropriate dots in the imaged area, moving with preset subsidiary velocities U,, are examined ( n = x , y, d). The velocities are selected to vary by a suitable number of discrete values in accordance with the discretization of the array receiver and also depending on the inter exposure time. Since the time between exposures is set constant, the velocities U~ are related to dots, which have been shifted
1 June 1992
in the image plane, continually progressing with each successive exposure. Assuming that x and y coincide respectively with Xo and Yo, the t-realization in a dot, which moves with subsidiary velocity Ux will have the following description. (1)
(~w(t)=(~o(Xo=Xo[U~(t)],Yo=Const).
(iii) The building of spatial cross-correlative functional dependencies is replaced by obtaining temporary instabilities of dots, moving with subsidiary velocities /-In. For every given velocity the relevant temporary instability has to be computed using equations, consisting of the sums of the squared differences between appropriate numbers of pixel values. Actually the intensity differences for every pair of pixels in the preselected directions are estimated to form the full number of temporary instabilities It, u" . Thus the relevant curves could be obtained. For the temporary instability at /.In=/.Ix we will have the relation: l(ttux) = ( (dOu~,/dt)2> 1
- At 2 (Oux(Vx, X ) - O v x ( V ~ - ~ x , x - 1 ) )
2,
(2)
where ~x, Vx, r represent the indexes of the current element of the first matrix, ~x and vx are integers, varying in this particular case from 1 to 480. From this relation one could find out that the dependencies i}/u,) should look like structure functions, that is why the result for the velocity is insensitive to the statistical inhomogeneity and instability of the atmospheric aerosol field [ 10 ]. (iv) After delivering the data for the temporary instability dependencies, the coordinates of the minima have to be found. The minimum of the curve for each of the temporary instabilities is obtained for a velocity U,, relevant to the real velocity V, in the considered direction. The main drift velocity is calculated by substituting the coordinates of the minima in formulae, where the technical features of the measuring system are included.
3. Experimental results The experimental set up used to put the method into practice comprises a CCD array receiver 17
Volume 90, number 1,2,3
OPTICS COMMUNICATIONS
(480X 388) with suitable optics, electronic system for data acquisition and preprocessing, and IBM/AT 386 compatible computer. The receiving optical system allows a wide range of angle of view variations, which makes it possible to investigate objects of different size. To carry out measurements, the system is adjusted in advance to capture the aerosol field with the whole image receiver surface. For diminishing the daylight background, a set of attenuative filters has been utilized. An array charge coupled device is used, possessing a modified control unit for selective adjustment of the device resolution, depending on the contrast of the picture. For a low contrast level the image receiver's sensitivity could be increased at the expense of its resolution. The registered image sequences are converted digitally by an electronic system and, properly sized, are fed into the computer via interface for further processing. Only the data required by the method, and not the whole frames are used. They are considerably less than the data used for velocity determination according to other methods, so no special requirements for the computer memory size exist. In fact the data from a selected row, column and the diagonal from x registered by the receiver images of the field are processed. The system software was designed on the basis of two algorithms. The overall system control and captured image transfer algorithm includes: (i) setting the initial data to operate the system, which comprises the number of the images to be registered, the inter exposure period and the distance to the object, (ii) after setting the initial data, the images are successively committed to frame buffer memory and are fed into the computer in the time between exposures, (iii) the entered data run the memory first and could be stored as a data file for their processing. The frame buffer memory addressing is accomplished in accordance with a computer command, followed again by the storage mode to register the next image. The algorithm for processing the collected realizations is based on the presented method of the temporary instabilities. The data corresponding to the movement in the preset directions are selected from the stored information. The relevant temporary instabilities are then calculated for each direction for positively and negatively oriented velocities. For 18
1 June 1992
higher precision, an approximation of the gained dependencies is conducted in the area of minima. After fixing the necessary parameters and their substitution in the formulae, the velocity components, modulus and the angle of the main drift in respect to the x axis in the image plane are calculated. In fig. 1 two processed images are presented, showing, at different moments, a statistically inhomogeneous object, which is a moving field of clouds. The total number of exposures used for the described method to operate was ten. The period between exposures is set so that the investigated field remains in the area of view during the time of measurement. The measurable velocity range depends on the exposure time and also on the time for every frame acquisition, the computer type and the software. In our case, the necessary time for the final result to be displayed in approximately 45 s when an AT 386 computer, provided with a co-processor, is utilized. A considerable time decrease could be achieved with software improvement and then the measurable velocity range would practically depend on the technical features of the receiving tract. A typical view of the dependencies I,t = f ( U , , ) for an experimentally gained time-spatial realization of an investigated moving field of clouds is shown in fig. 2. The velocities U, are normalized to Up=An~ At, where An is the discretization of the receiver and At is the period between exposures. The experiments on the velocity measurement have been conducted with cloud fields in different weather conditions on the territory of Sofia. The altitude of the field above the receiver was measured by conventional means to fix the distance to the clouds and
-,¢. • 4
at
!:
Fig. 1. The imagesof an investigatedcloud field in two successive moments as they have been displayed after capturing and preprocessing.
Itt 111 lO~
. . . . -
91
~-
for Ud
for Uy for Ux
x
/
M
~
0.
o
O
,,/
o
o
o
~.
:
. tT~ ~,7.~a
n' 4i
o
o
, ~
<~ 6i
.
~a,o. -
/.;
--.
i
1 June 1992
OPTICS COMMUNICATIONS
Volume 90, number 1,2,3
',,
tTai
tTa, J~a~
m~o
TII~ ( h a n i n )
2
1-~'"'-'~'""-:'4"""~"~J-'"~~--~ " E ~ b
Un/Uo
Fig. 4. The variations of the cloud field velocity direction compared with the averaged wind direction at the altitude of the clouds.
SUBS. VELOCITIES
Fig. 2. The temporary instability dependencies for three preset directions in the image plane.
"d
51 o
~.~ 0
'
o o
o
o
o
o
>
20%, while the deviation in the direction never exceeded 5%. The bigger deviation in the velocity values could be explained by inaccuracy in the determination of the clouds altitude with the available tools, which has less effect on the direction, but is very important for the precision in obtaining the modulus. However the method gives complete information about velocity changes over comparatively short time intervals, which can not be obtained by conventional means.
I?'.~ I?'~6 I?'~B l?'~l/?.n& I?~2"¢ 17aiG
TIME (hmain) Fig. 3. The fluctuations of the cloud field velocity values compared with the averaged speed of wind at the altitude of the clouds.
it varied from 500 to 6000 meter. We have considered only parallel translation above the ground. The experimental results have been compared with the data from conventional sources. When the system operates, permanent information about the velocity and its fluctuations could be provided. Part of the results from the conducted measurements are shown in figs. 3 and 4, where are presented the moment values of the cloud field velocity and the variations of the direction for a fixed period of time. They have been compared with the speed of the wind at the altitude of the clouds, averaged for the period of the measurements and provided by a kitoon. The measurements for cloud velocity determination were carried out every three minutes. The presented data have been received during a period of rapid changes in the atmosphere dynamics, so the fluctuations of the velocity are considerable. The average velocity, measured with conventional means differed from the average velocity, obtained by the method by up to
4. Summary
and conclusions
An information processing technique for velocity determination of statistically inhomogeneous objects has been experimentally varified for moving cloud fields. The velocity measurements have been conducted by collecting time-spatial realizations of the imaged field, which does not change its character during the gathering time. The data of a fixed row, column and the diagonal from every frame of the image sequence are selected and they are used to develop the temporary instabilities for separate dots of the field. The modulus and the direction of the velocity vector are determined after fixing the coordinates of the minimum value for every gained dependence and after substitution of the coordinates in formulae drawn beforehand. To obtain the velocity, additional information about the distance to the object is necessary in advance. The proposed system could also operate independently. This could be accomplished by incorporating a pulse laser to the system, whose operation is adjusted to the frame gathering mode. Using a 19
Volume 90, number 1,2,3
OPTICS COMMUNICATIONS
laser, it is possible to solve the problem of fixing the distance promptly, to provide measurements at different distances along the sounding range, and to measure velocity of objects with low contrast. References [ 1 ] R. Meynart, Appl. Optics 22 (1983) 535. [ 2 ] P.V. Farrell and D. Goetsch, Optics Lett. 14 ( 1989 ) 978. [ 3 ] W. Arnold and K.D. Hinsch, Appl. Optics 28 ( 1989 ) 726.
20
1 June 1992
[4] Y.-C. Cho, Appl. Optics 28 (1989) 740. [ 5 ] I. Grant and J.H. Qiu, Appl. Optics 29 (1990) 4327. [6] B. Frieden and C. Zoltany, Appl. Optics 28 (1989) 652. [ 7 ] V.A. Mitev, E.S. Ferdinandov and E.V. Stoykova, paper $6. 14 Int. Laser Radar Conf. (Innichen-San Candido, Italy, 1988). [8]B.H. Briggs, MAP Handbook 13 ed. R.A. Vincent (SCOSTEP, Urbana, Illinois, 1984) p. 166. [ 9 ] V.E. Zuev, ed., Application of the Correlative Methods in Atmosphere Optics (Nauka, Moscow, 1983 ) in Russian. [10] E. Ferdinandov and E. Stoykova, Bulg. J. Phys. l l (1984) 58.
OPTICS COM MUNICATIONS
Image velocimetry of atmospheric inhomogeneities using a statistical approach V.A. M i t e v a n d G.I. Sokolinov Bulgarian Academy of Sciences, Institute of Electronics, Sofia 1784, Bulgaria Received 10 July 1991; revised manuscript received 16 December 1991
Velocity measurements of imaged cloud fields have been conducted by gathering time-spatial realizations. Properly selected data are used to produce at least three dependencies of temporary instabilities for moving dots in the imaged area. The modulus and the direction of the velocityvector are determined after fixingthe coordinates of the minimum value for every gained dependence. Two algorithms for data acquisition and processing have been developed. Consecutive measurementsfor cloud velocity determination have been carried out in three-minute periods.
1. Introduction
The registration and processing of image sequences is applied with an increasing rate in the remote sensing and control for measuring the velocity and estimating the motion of different objects. The main advantage of this technique is in the possibility for express analysis of large spatial areas with a high information gain. The double-exposure photography methods are often used to obtain the velocity of objects, including air flows [ 1 ]. If one investigates a seeded flow movement, depending on the panicle dimensions and concentration, the velocity measurements are accomplished by processing specklegrams or by tracing out different particles on the registered images. The optical methods for speckle-pattern processing are based on the two-dimensional Fourier transformation. It is applied to tiny separate areas of the image to produce interference patterns, which contain information about the movement of the object [ 1-3 ]. The processing of the interference patterns, as well as the direct determination of the velocity vectors by registration of images [ 4-7 ] could be carried out using different digital methods. The velocity vector could be also obtained without producing interferograms optically [4 ]. After digitizing the registered images and adding their relevant pixel intensities, the information is analyzed by applying a digital Fourier 16
transformation. Digital filtering was used to demonstrate selection of particles moving with equal velocities [ 5 ]. An algorithm, built on the basis of crosscorrelation between two successively captured images was also used for obtaining the velocity by estimating the drift of particle clumps [ 6 ]. A similar correlation method, used as a basis for designing an imaging system for passive remote sensing of cloud fields has been described earlier [ 7], However, the imaged field is treated as a moving object, where individual particles or clumps are not considered. The main drift velocity vector is set by the position of the global correlation maximum, which is obtained for different couples of registered images. Using an image receiver for the implementation of the method also provides the measurement of moment velocity values. Correlation remote sensing methods give an opportunity to measure both the main drift velocity of aerosol inhomogeneities and their statistical features (life time, space scales and orientation) as well [ 8,9 ]. The following obstacles oppose this universality: huge quantity data processing, the necessity for many sophisticated computing operations, strong accuracy dependence of the result on the statistical inhomogeneity and instability of the aerosol field. The speed of data handling and the measurement rate could be considerably increased by a kind of simplified statistical information processing, which
0030-4018/92/$ 05.00 © 1992 Elsevier Science Publishers B.V. All fights reserved.
Volume 90, number 1,2,3
OPTICS COMMUNICATIONS
however provides determination only of the velocity [ 10 ]. Developing this idea, we have put into practice a method for remote measurement of the velocity by capturing time-spatial realizations of the investigated aerosol field, using an image array receiver, and by building the temporary instabilities of these realizations.
2. A brief method description The idea of the method has been described in detail earlier in ref. [ 10]. Following is a summary of the main points. (i) In the plane of the receiver three coordinate systems are introduced: one fixed relative to the imaging camera (Xo, Yo), one moving with the real velocity of the aerosol inhomogeneities (x~, Yv) and another (x,, y,) moving with a variable preset velocity. K images of the investigated field are registered in different moments &, ( x = 1, 2, ..., k) using successive constant-time exposures, separated by equal time periods. All the images collected in one measurement cycle form a time-spatial realization ot = ¢o (Xo, Yo, t), which consists of the image-data developed in time. (ii) The time-spatial realization a=q~o(Xo, Yo, t) is interpreted as time-dependent only (t) realizations of clots in the image field moving with velocities U, in the plane (Xo, Yo) and motionless in the coordinate system (x,, y,). These t-realizations are achieved after suitable selection of the data from every frame in three preselected directions (line x, column y and the diagonal d of the image receiver), so that three matrices are constructed. Their dimensions are fixed by the number of pixels in the relevant direction and by the number of exposures, used to form one time-spatial realization. The directions chosen could also be arbitrarily selected as long as they are not permitted to be parallel. The essential idea is that appropriate dots in the imaged area, moving with preset subsidiary velocities U,, are examined ( n = x , y, d). The velocities are selected to vary by a suitable number of discrete values in accordance with the discretization of the array receiver and also depending on the inter exposure time. Since the time between exposures is set constant, the velocities U~ are related to dots, which have been shifted
1 June 1992
in the image plane, continually progressing with each successive exposure. Assuming that x and y coincide respectively with Xo and Yo, the t-realization in a dot, which moves with subsidiary velocity Ux will have the following description. (1)
(~w(t)=(~o(Xo=Xo[U~(t)],Yo=Const).
(iii) The building of spatial cross-correlative functional dependencies is replaced by obtaining temporary instabilities of dots, moving with subsidiary velocities /-In. For every given velocity the relevant temporary instability has to be computed using equations, consisting of the sums of the squared differences between appropriate numbers of pixel values. Actually the intensity differences for every pair of pixels in the preselected directions are estimated to form the full number of temporary instabilities It, u" . Thus the relevant curves could be obtained. For the temporary instability at /.In=/.Ix we will have the relation: l(ttux) = ( (dOu~,/dt)2> 1
- At 2 (Oux(Vx, X ) - O v x ( V ~ - ~ x , x - 1 ) )
2,
(2)
where ~x, Vx, r represent the indexes of the current element of the first matrix, ~x and vx are integers, varying in this particular case from 1 to 480. From this relation one could find out that the dependencies i}/u,) should look like structure functions, that is why the result for the velocity is insensitive to the statistical inhomogeneity and instability of the atmospheric aerosol field [ 10 ]. (iv) After delivering the data for the temporary instability dependencies, the coordinates of the minima have to be found. The minimum of the curve for each of the temporary instabilities is obtained for a velocity U,, relevant to the real velocity V, in the considered direction. The main drift velocity is calculated by substituting the coordinates of the minima in formulae, where the technical features of the measuring system are included.
3. Experimental results The experimental set up used to put the method into practice comprises a CCD array receiver 17
Volume 90, number 1,2,3
OPTICS COMMUNICATIONS
(480X 388) with suitable optics, electronic system for data acquisition and preprocessing, and IBM/AT 386 compatible computer. The receiving optical system allows a wide range of angle of view variations, which makes it possible to investigate objects of different size. To carry out measurements, the system is adjusted in advance to capture the aerosol field with the whole image receiver surface. For diminishing the daylight background, a set of attenuative filters has been utilized. An array charge coupled device is used, possessing a modified control unit for selective adjustment of the device resolution, depending on the contrast of the picture. For a low contrast level the image receiver's sensitivity could be increased at the expense of its resolution. The registered image sequences are converted digitally by an electronic system and, properly sized, are fed into the computer via interface for further processing. Only the data required by the method, and not the whole frames are used. They are considerably less than the data used for velocity determination according to other methods, so no special requirements for the computer memory size exist. In fact the data from a selected row, column and the diagonal from x registered by the receiver images of the field are processed. The system software was designed on the basis of two algorithms. The overall system control and captured image transfer algorithm includes: (i) setting the initial data to operate the system, which comprises the number of the images to be registered, the inter exposure period and the distance to the object, (ii) after setting the initial data, the images are successively committed to frame buffer memory and are fed into the computer in the time between exposures, (iii) the entered data run the memory first and could be stored as a data file for their processing. The frame buffer memory addressing is accomplished in accordance with a computer command, followed again by the storage mode to register the next image. The algorithm for processing the collected realizations is based on the presented method of the temporary instabilities. The data corresponding to the movement in the preset directions are selected from the stored information. The relevant temporary instabilities are then calculated for each direction for positively and negatively oriented velocities. For 18
1 June 1992
higher precision, an approximation of the gained dependencies is conducted in the area of minima. After fixing the necessary parameters and their substitution in the formulae, the velocity components, modulus and the angle of the main drift in respect to the x axis in the image plane are calculated. In fig. 1 two processed images are presented, showing, at different moments, a statistically inhomogeneous object, which is a moving field of clouds. The total number of exposures used for the described method to operate was ten. The period between exposures is set so that the investigated field remains in the area of view during the time of measurement. The measurable velocity range depends on the exposure time and also on the time for every frame acquisition, the computer type and the software. In our case, the necessary time for the final result to be displayed in approximately 45 s when an AT 386 computer, provided with a co-processor, is utilized. A considerable time decrease could be achieved with software improvement and then the measurable velocity range would practically depend on the technical features of the receiving tract. A typical view of the dependencies I,t = f ( U , , ) for an experimentally gained time-spatial realization of an investigated moving field of clouds is shown in fig. 2. The velocities U, are normalized to Up=An~ At, where An is the discretization of the receiver and At is the period between exposures. The experiments on the velocity measurement have been conducted with cloud fields in different weather conditions on the territory of Sofia. The altitude of the field above the receiver was measured by conventional means to fix the distance to the clouds and
-,¢. • 4
at
!:
Fig. 1. The imagesof an investigatedcloud field in two successive moments as they have been displayed after capturing and preprocessing.
Itt 111 lO~
. . . . -
91
~-
for Ud
for Uy for Ux
x
/
M
~
0.
o
O
,,/
o
o
o
~.
:
. tT~ ~,7.~a
n' 4i
o
o
, ~
<~ 6i
.
~a,o. -
/.;
--.
i
1 June 1992
OPTICS COMMUNICATIONS
Volume 90, number 1,2,3
',,
tTai
tTa, J~a~
m~o
TII~ ( h a n i n )
2
1-~'"'-'~'""-:'4"""~"~J-'"~~--~ " E ~ b
Un/Uo
Fig. 4. The variations of the cloud field velocity direction compared with the averaged wind direction at the altitude of the clouds.
SUBS. VELOCITIES
Fig. 2. The temporary instability dependencies for three preset directions in the image plane.
"d
51 o
~.~ 0
'
o o
o
o
o
o
>
20%, while the deviation in the direction never exceeded 5%. The bigger deviation in the velocity values could be explained by inaccuracy in the determination of the clouds altitude with the available tools, which has less effect on the direction, but is very important for the precision in obtaining the modulus. However the method gives complete information about velocity changes over comparatively short time intervals, which can not be obtained by conventional means.
I?'.~ I?'~6 I?'~B l?'~l/?.n& I?~2"¢ 17aiG
TIME (hmain) Fig. 3. The fluctuations of the cloud field velocity values compared with the averaged speed of wind at the altitude of the clouds.
it varied from 500 to 6000 meter. We have considered only parallel translation above the ground. The experimental results have been compared with the data from conventional sources. When the system operates, permanent information about the velocity and its fluctuations could be provided. Part of the results from the conducted measurements are shown in figs. 3 and 4, where are presented the moment values of the cloud field velocity and the variations of the direction for a fixed period of time. They have been compared with the speed of the wind at the altitude of the clouds, averaged for the period of the measurements and provided by a kitoon. The measurements for cloud velocity determination were carried out every three minutes. The presented data have been received during a period of rapid changes in the atmosphere dynamics, so the fluctuations of the velocity are considerable. The average velocity, measured with conventional means differed from the average velocity, obtained by the method by up to
4. Summary
and conclusions
An information processing technique for velocity determination of statistically inhomogeneous objects has been experimentally varified for moving cloud fields. The velocity measurements have been conducted by collecting time-spatial realizations of the imaged field, which does not change its character during the gathering time. The data of a fixed row, column and the diagonal from every frame of the image sequence are selected and they are used to develop the temporary instabilities for separate dots of the field. The modulus and the direction of the velocity vector are determined after fixing the coordinates of the minimum value for every gained dependence and after substitution of the coordinates in formulae drawn beforehand. To obtain the velocity, additional information about the distance to the object is necessary in advance. The proposed system could also operate independently. This could be accomplished by incorporating a pulse laser to the system, whose operation is adjusted to the frame gathering mode. Using a 19
Volume 90, number 1,2,3
OPTICS COMMUNICATIONS
laser, it is possible to solve the problem of fixing the distance promptly, to provide measurements at different distances along the sounding range, and to measure velocity of objects with low contrast. References [ 1 ] R. Meynart, Appl. Optics 22 (1983) 535. [ 2 ] P.V. Farrell and D. Goetsch, Optics Lett. 14 ( 1989 ) 978. [ 3 ] W. Arnold and K.D. Hinsch, Appl. Optics 28 ( 1989 ) 726.
20
1 June 1992
[4] Y.-C. Cho, Appl. Optics 28 (1989) 740. [ 5 ] I. Grant and J.H. Qiu, Appl. Optics 29 (1990) 4327. [6] B. Frieden and C. Zoltany, Appl. Optics 28 (1989) 652. [ 7 ] V.A. Mitev, E.S. Ferdinandov and E.V. Stoykova, paper $6. 14 Int. Laser Radar Conf. (Innichen-San Candido, Italy, 1988). [8]B.H. Briggs, MAP Handbook 13 ed. R.A. Vincent (SCOSTEP, Urbana, Illinois, 1984) p. 166. [ 9 ] V.E. Zuev, ed., Application of the Correlative Methods in Atmosphere Optics (Nauka, Moscow, 1983 ) in Russian. [10] E. Ferdinandov and E. Stoykova, Bulg. J. Phys. l l (1984) 58.