=Paper=
{{Paper
|id=Vol-2210/paper43
|storemode=property
|title=3d synthetic aperture radar image
|pdfUrl=https://ceur-ws.org/Vol-2210/paper43.pdf
|volume=Vol-2210
|authors=Anatolii Leukhin,Alexandr Rozentsov,Vladimir Bezrodnyi,Aleksei Voronin,Denis Karasev,Natalia Kokovihina
}}
==3d synthetic aperture radar image==
https://ceur-ws.org/Vol-2210/paper43.pdf
3d synthetic aperture radar image
A N Leukhin1, A A Rozentsov2, V I Bezrodnyy1, A A Voronin1, D Yu Karasev2
and N A Kokovihina1
1
Mari State University, Lenin square 1, Yoskar-Ola, Russia, 424000
2
Volga State University of Technology, Lenin square 3, Yoskar-Ola, Russia, 424000
Abstract. Synthetic aperture radar (SAR) is a coherent active microwave imaging method. In
remote sensing it is used for mapping the scattering properties of the Earth’s surface in the
respective wavelength domain. The algorithms for the formation of 3D radar images in multi-
position interferometric systems for remote sensing of the Earth are considered. Examples of
reconstruction of the relief map for systems with one and two transmit antenna are presented.
1. Introduction
The application of interferometric data processing to obtain information about the terrain and its
changes, implementation of high resolution (1-3 m) regimes have become the main trends in the
development of modern radar systems for space observation. Such processing of space-based synthetic
aperture radar`s data includes the following steps: synthesis a pair of complex radar images of the
same surface region, their spatial overlap with the formation of an interferogram; phase noise filtering
on the obtained interferogram; deployment of the phase of the interferogram and its full geocoding
(recalculation of the values of the expanded phase in the values of the relief heights and the transition
from the flight coordinate system to any cartographic projection).
The purpose of this paper is to review the methods of interferometric data processing to obtain 3d
synthetic radar image of a surface model.
It is necessary to first describe the basics of 3d SAR imaging and explain its features.
A second antenna is installed on an aircraft at a certain distance from the first antenna in order to
enable forming a three-dimensional map of the underlying surface mode in synthetic aperture radar.
As a rule, the spacing can be carried out either in height or in a horizontal plane perpendicular to the
direction of flight.
There are several options for the operation of SAR in 3D mode [1]:
1. Radiation is performed through both antennas by turns.
2. Radiation is made through one antenna (for example, A1 ), and receiving is performed through
two antennas A1 and A2 .
3. On the radiation, the transmitter operates on one of its own antennas ( A3 ), the receivers have
two own antennas A1 and A2 .
3D images of surface are analysed by hypertrace transformation [2].
Let's consider the basic geometrical relations necessary for calculation of objects` height in SAR
3D mode.
IV International Conference on "Information Technology and Nanotechnology" (ITNT-2018)
Image Processing and Earth Remote Sensing
A N Leukhin, A A Rozentsov, V I Bezrodnyy, A A Voronin, D Yu Karasev and N A Kokovihina
2. “Two transmitters, two receivers” system
Figure 1 shows the basic geometric equations for the 3D SAR system, for the case when the aircraft is
equipped with two transmitter and two receivers, operating through its own spaced from each other
antenna.
Using the basis of the Pythagorean theorem we can write:
( H1 h) r1 R1
2 2 2
( H 2 h) (r1 d ) R2
2 2 2
(1)
Values of the heights H 1 and H 2 of the antennas and antenna spacing d in the horizontal plane
can be considered known while SAR is working. Also known and sloped range R1 and R2 . You need
to find the horizontal distance r1 and the height of the object h . Before solving the equation (1) we can
first calculate r1 and then determine h or vice versa. The solution to the system is determined by the
ratio between the values d and H1 H 2 . If H1 H 2 d you choose the first method, otherwise
the second. Two solutions are obtained when you use each method. A preference in favor of a solution
that gives value r1 least different from the values of the horizontal range, designed for zero height
r1(0) ( R12 H12 )1 / 2 , i.e. r1 r1(0) min [3].
Figure 1. Basic geometric equations in “two transmitters, two receivers” system.
Possible solutions of the equation (1) are defined by equations (2) and (3):
r1 ( H 12 d H 2 2 d R12 d R 2 2 d d 3 2 H 1 H 2 d
( H 12 2 H 1 H 2 H 2 2 R12 2 R1 R 2 R 2 2 d 2 )1 / 2
(2 H 1 H 2 H 12 H 2 2 R12 2 R1 R 2 R 2 2 d 2 )1 / 2 (2)
1
( H 2 H 1)) ;
2 ( H 12 2 H 1 H 2 H 2 2 d 2 )
H 2 2 H 12 R12 R 2 2 d 2 2 r1 d
h
2 H1 2 H 2
h ( H 1 d 2 H 2 d 2 H 13 H 23 H 1 H 2 2 H 12 H 2
H 1 R12 H 1 R 2 2 H 2 R12 H 2 R 2 2 d
( H 12 2 H 1 H 2 H 2 2 R12 2 R1 R 2 R 2 2 d 2 )1 / 2
(2 H 1 H 2 H 12 H 2 2 R12 2 R1 R 2 R 2 2 d 2 )1 / 2 ) (3)
1
;
2 ( H1 2 H1 H 2 H 22 d 2 )
2
R12 R 2 2 d 2 ( H 2 h) 2 ( H 1 h) 2
r
2d
IV International Conference on "Information Technology and Nanotechnology" (ITNT-2018) 331
Image Processing and Earth Remote Sensing
A N Leukhin, A A Rozentsov, V I Bezrodnyy, A A Voronin, D Yu Karasev and N A Kokovihina
On the practice ranges R1 and R2 are known with an item resolution accuracy, so the calculations
of value h and r1 use value R R2 R1 , calculated on the basis of the measurement result of the
phase difference
( w)
R 2 1, (4)
4 4
where 1 and 2 - phases of the signals received from the first and second antennas, respectively; -
wave`s length.
Because the value of the phase shift is in the range [0,2 ) , as a rule, there is ambiguity of the
measurement values R . To fix it uses the "unwrap" phase. Consider possible approaches to its
implementation [4].
The first approach is based on the preliminary construction of the dependence of phase shifts to the
zero level, depending on slant range to the antenna A1 [5]:
0 R1 4R 0 R1 / 4 ((H 2 2 ((R12 H12 )1/ 2 d ) 2 )1/ 2 R1 ) / (5)
Then the value of the phase shift u R used to calculate the difference between the sloping
1
distances, determined from the relationship:
0 R1
u R1 w trunc 2
(6)
2
The value of the slant range R2 used for the calculation h and r1 is determined from the relation:
u
R2 R1 2m (7)
4
To determine the value m , you can use the following approach. Typically, the height difference
between adjacent pixels is relatively small and we can assume that the height of the object in some
neighborhood is constant. Presented according to m estimates of the altitude differences in the
neighboring pixels have a pronounced minimum, and calculations show that this minimum is achieved
when the value of the parameter m̂ corresponding to the true values of the altitude and slant range.
The algorithm of the calculation value m̂ is the following:
1. Around the current image point with coordinates x0 , y0 , set the gate;
2. Sets the range of values m : m mmin ...mmax
3. For each point in the gate with coordinates x , y , a values rx, y and hx, y are calculated with
current value m ;
4. Calculate total measurement error of the heights and horizontal distances. Terms y1 y0 and
y2 y0 take into account the current offset of pixels in the horizontal range:
x0 dx y0 dy x0 dx y0 dy
hm hx1, y1 hx2 , y2
x1 x0 dx y1 y0 dy x2 x0 dx y2 y0 dy
x0 dx y0 dy x0 dx y0 dy
rm y x1, x 2, y1, y 2 (8)
x1 x0 dx y1 y0 dy x2 x0 dx y2 y0 dy
y x1, x 2, y1, y 2 rx1, y1 y1 y0 rx2 , y2 y 2 y0
5. As a result, selects the value m̂ at which
hmˆ min , кmˆ min (9)
Because of spacing antennas, the resulting images have some mutual shift, and its magnitude will
depend on the range. In this regard, before calculating the elevation, you must perform the mutual
correction of the shifts of image elements. For this calculate values of distances R2 corresponding to
IV International Conference on "Information Technology and Nanotechnology" (ITNT-2018) 332
Image Processing and Earth Remote Sensing
A N Leukhin, A A Rozentsov, V I Bezrodnyy, A A Voronin, D Yu Karasev and N A Kokovihina
the range R1 on the zero level and overwrite the elements of the second array with the ranges R2 in
cells that correspond to values in the range R1 [6]:
J Rкор 2
,x J R ,x
1 2 (10)
R2 ( H 2 ((R12 H12 )1 / 2 d ) 2 )1 / 2
2
where J R22, x - image from the second antenna.
Figure 2 shows an example of the recovery bump maps for the considered case when the following
system parameters: H1 H 2 10m , d 5m the maximum altitude of the relief 5m.
(a) (b)
Figure 2. An example of the recovery of the terrain surface. a – synthesized image, b – 3D relief of
the surface.
3. “Two transmitters, one receiver” system
Figure 3 shows the basic geometric equations for the 3D SAR system, for the case when an aircraft
equipped with one transmitter operating, for example, via an antenna A1 , and two receivers, operating
through its own separated antennas A1 and A2 .
In this system a signal between antennas A1 and A2 the point on the object surface takes place in
two ways S1 2R1 and S 2 R1 R2 respectively. In the simulation of the hologram samples of the
signal in the first image is recorded with a pixel corresponding to the distance R1 , and a second
R R2
hologram pixel 1 .
2
Figure 3. Basic geometric equations in “two transmitters, one receiver” system.
The value of the path S 2 is determined based on the known path S1 and phase difference due to
antenna spacing:
IV International Conference on "Information Technology and Nanotechnology" (ITNT-2018) 333
Image Processing and Earth Remote Sensing
A N Leukhin, A A Rozentsov, V I Bezrodnyy, A A Voronin, D Yu Karasev and N A Kokovihina
m, m ...,2,1,0,1,2,...
S 2 S1 (11)
2
Knowing the values of the parameters S1 , S 2 , H1 , H 2 , d , you can find value and a horizontal
range r1 :
D 2 (d 2 (d 2 S12 2 H 12 S 2 2 2 H 2 2 S 2 2 2 S1 d 2 S 2 S 2 4 H 2 2 S12
4 H 13 H 2 2 d 2 S 2 2 H 12 S12 d 4 2 H 2 2 d 2 H 14 H 2 4 2 H 12 d 2
6 H 12 H 2 2 2 S1 S 2 H 12 2 S1 S 23 4 H 1 H 2 d 2 4 H 1 H 23 4 H 1 H 2 S12
(12)
4 H 1 H 2 S1 S 2 2 H 2 2 S1 S 2 4 H 1 H 2 S 2 2 S12 S 2 2 ))0.5
H 1 S1 S 2 H 2 d 2 H 12 H 2 H 13 H 23 H 1 d 2 H 2 S 2 2
h
2 ( H 12 H 2 2 d 2 2 H 1 H 2)
H 1 S 2 2 H 2 S1 S 2 H 1 H 2 2 D 2
2 ( H 12 H 2 2 d 2 2 H 1 H 2)
As in the first case, measuring the phase shift may be ambiguous. The dependence of phase shifts on
the zero level from the slant range to the antenna A1 is described by the expression:
( H 2 2 ((R12 H12 )1 / 2 d ) 2 )1 / 2 R1
0 R1 2 (13)
Then the value of the phase shift u R1 is used to calculate the difference between the sloping
distances is determined from the equation (6). Path S 2 is used for the calculation h and r1 is
determined from the expression:
u 2m
S 2 2 R1 (14)
2
The value m is chosen by the equation (9).
Still from the spacing antennas, the elements of the resulting images can have some mutual shift.
To compensate for this shift is necessary to perform the image correction according to the relation [7]:
J Rкор 2
,x J R R (15)
1 1 2 ,x
2 ,
where R2 is computed as in equation (10).
Figure 4 shows an example of the recovery bump maps for the considered case when the following
system parameters H1 H 2 10m , d 5m the maximum altitude of the relief 5m.
Figure 4. Synthesized 3D image of the surface.
4. Conclusions
Solution of a problem of restoration of a landscape`s in a synthetic aperture radar at various
configuration of a reception-transmitting path is considered in this work. An original phase
unwrapping algorithm based on joint minimization of the estimating error of object`s height and
IV International Conference on "Information Technology and Nanotechnology" (ITNT-2018) 334
Image Processing and Earth Remote Sensing
A N Leukhin, A A Rozentsov, V I Bezrodnyy, A A Voronin, D Yu Karasev and N A Kokovihina
sloped range in neighboring pixels of the image is proposed. Examples of the restored 3D images are
presented.
5. References
[1] Richard B, Philipp H 1998 Synthetic aperture radar interferometry Inverse Problems 14(4) R1-
R54
[2] Fedotov N, Syemov A and Moiseev A 2016 Analysis of conditions that influence the properties
of the consructed 3d-image Computer Optics 40(6) 887-894 DOI: 10.18287/2412-6179-2016-
40-6-887-894
[3] Kobernichenko V and Sosnovsky A 2012 Interferometer data processing space radar imagery of
high resolution Physics of Wave Processes and Radio Engineering Systems 15(3) 75-83
[4] Vidal-Pantaleoni A, Rafael O and Miguel F 1999 A Comparison of Phase Unwrapping
Techniques in Synthetic Aperture Radar Interferometry IEEE International Geoscience and
Remote Sensing Symposium 1354-1356
[5] Osmanoglu B and Dixon T 2011 On the importance of path for phase unwrapping in synthetic
aperture radar interferometry Applied Optics 50(19) 3205-3220
[6] Richards M 2007 A Beginner’s Guide to Interferometric SAR Concepts and Signal Processing
IEEE A & E Systems Magazine 22(9) 5-29
[7] Sosnovsky A and Kobernichenko V 2012 Phase unwrapping algorithms investigation in digital
elevation maps generation using space-based InSAR Izvestiya of the Higher Educational
Establishments of Russia. Radio electronics 7 84-92
Acknowledgments
The work is executed at financial support of the Ministry of Education and Science of the Russian
Federation, project No. 2.2226.2017/Project Part and project No. 2.9140.2017/Basic Part. The work is
performed under financial support of Russian Found of Basic Research, research project No. 15-07-
99514.
IV International Conference on "Information Technology and Nanotechnology" (ITNT-2018) 335