Interpolation-free three-dimensional active millimeter wave imaging method and system and imaging equipment
阅读说明：本技术 无插值三维主动毫米波成像方法及系统、成像设备 (Interpolation-free three-dimensional active millimeter wave imaging method and system and imaging equipment ) 是由 林川 臧杰锋 于 2019-09-24 设计创作，主要内容包括：本发明公开了一种无插值三维主动毫米波成像方法及系统、储存介质、成像设备,结合傅立叶变换、解线频调相位补偿、并行计算等技术,基于宽带线性调频三维主动毫米波成像系统参数与采集到的实际测量数据实现三维成像；该方法不需要三维主动毫米波全息成像算法所用到的Stolt插值操作,避免了大量的插值运算及额外的插值误差,减少成像过程的计算量,可提高主动毫米波安检成像效率。(The invention discloses interpolation-free three-dimensional active millimeter wave imaging method and system, a storage medium and imaging equipment, which are combined with technologies such as Fourier transform, demodulation frequency modulation phase compensation, parallel computation and the like to realize three-dimensional imaging based on parameters of a broadband linear frequency modulation three-dimensional active millimeter wave imaging system and collected actual measurement data.)
1, A method for forming millimeter wave without interpolation, which is characterized in that the method comprises:
acquiring th echo data of an imaging object, wherein the th echo data comprise line-breaking tone signals s (x) corresponding to the imaging object which are acquired at equal intervals on a receiving plane according to preset sampling time intervalsIs connected with，yIs connected withT), wherein the receiving plane and the imaging subject are located in the same three-dimensional coordinate system, the three-dimensional coordinate system including an x-axis, a y-axis, and a Z-axis, the receiving plane being Z ═ Z1，(xIs connected with，yIs connected with) Representing the position coordinates of the sampling points on the receiving plane, wherein t is a time domain;
performing phase compensation on the th echo data to obtainObtaining second echo data sc(xIs connected with，yIs connected withK); wherein the content of the first and second substances,
based on the reference distance used by the line-off tone modulation signal in the line-off tone modulation process, correcting the second echo data to obtain third echo data sd(xIs connected with，yIs connected with，k)；
Performing two-dimensional fast Fourier transform on the third echo data on the receiving plane to obtain fourth echo data Sd(kx，kyK); wherein k isxDenotes the component of k in the x-direction, kyRepresents the component of k in the y-direction;
after the fourth echo data is compensated, k is related toxAnd kyTo obtain fifth echo data fk(xEyes of a user，yEyes of a user，zEyes of a user)；
F corresponding to different values of wave number k in the fifth echo datak(xEyes of a user，yEyes of a user，zEyes of a user) Accumulating to obtain the scattering coefficient f (x) of the imaging objectEyes of a user，yEyes of a user，zEyes of a user)；
And outputting the scattering coefficient of the imaging object, and enabling the scattering coefficient to generate a reconstructed image.
2. The method of claim 1, wherein the de-line tone signal comprises:
wherein the content of the first and second substances,
f(xeyes of a user，yEyes of a user，zEyes of a user) For the imaging object in (x)Eyes of a user，yEyes of a user，zEyes of a user) The scattering coefficient of (d); rΔ＝R-Rref，RrefFor the reference distance used by the dechirp signal during the dechirp process,representing the distance, T, between the position of the imaging subject and the equivalent transmit-receive position of the receiving planepJ is the pulse width of the de-line tone signal and is an imaginary unit.
3. The method of claim 2, wherein said phase compensating said th echo data to obtain second echo data sc(xIs connected with，yIs connected withK), specifically including:
and performing fast Fourier transform on the th echo data in a t dimension to obtain:
S(xis connected with，yIs connected with，ξ)＝FFT[s(xIs connected with，yIs connected with，t)]Wherein ξ denotes frequency;
at dimension ξ, pair S (x)Is connected with，yIs connected withξ) to obtain:
to Sc(xIs connected with，yIs connected withξ) is inverse fast fourier transformed in ξ dimensions to yield:
let fd＝fc+γt，
4. the method of claim 3, wherein the second echo data is modified based on a reference distance used by the line-off tone signal during a line-off tone to obtain third echo data sd(xIs connected with，yIs connected withK), specifically including:
5. the method of claim 4, wherein compensating the fourth echo data for k is performedxAnd kyTo obtain fifth echo data fk(xEyes of a user，yEyes of a user，zEyes of a user) The method specifically comprises the following steps:
wherein k iszRepresenting the component of k in the z-direction,
6. the method of claim 1, wherein said performing a two-dimensional fast fourier transform of said third echo data on said receiving plane obtains fourth echo data Sd(kx，kyK), further comprising:
for different k, the third echo data is simultaneously processed with x in a parallel computing modeIs connected withAnd yIs connected withObtaining fourth echo data S by two-dimensional fast Fourier transformd(kx，ky，k)。
7. The method of claim 5, wherein compensating the fourth echo data for k is performedxAnd kyTo obtain fifth echo data fk(xEyes of a user，yEyes of a user，zEyes of a user) The method also comprises the following steps:
for different k and zEyes of a userPerforming compensation processing on the fourth echo data and k in parallel computing mannerxAnd kyTo obtain fifth echo data fk(xEyes of a user，yEyes of a user，zEyes of a user)。
8, kinds of no interpolation three-dimensional initiative millimeter wave imaging system, characterized by, includes:
a data acquisition module for acquiring th echo data of an imaging object, wherein the th echo data comprises a demodulation line tone signal s (x) corresponding to the imaging object which is acquired at equal intervals on a receiving plane according to a preset sampling time intervalIs connected with，yIs connected withT), wherein the receiving plane and the imaging subject are located in the same three-dimensional coordinate system, the three-dimensional coordinate system including an x-axis, a y-axis, and a Z-axis, the receiving plane being Z-Z1, (x) whereinIs connected with，yIs connected with) Representing the position coordinates of the sampling points on the receiving plane, wherein t is a time domain;
a compensation module for performing phase compensation on the th echo data to obtain second echo data sc(xIs connected with，yIs connected withK); wherein the content of the first and second substances,
a correction module, configured to correct the second echo data based on a reference distance used by the line-off tone modulation signal in the line-off tone modulation process, so as to obtain third echo data sd(xIs connected with，yIs connected with，k)；
A Fourier transform module for performing two-dimensional fast Fourier transform on the third echo data on the receiving plane to obtain fourth echo data Sd(kx，kyK); wherein k isxDenotes the component of k in the x-direction, kyRepresents the component of k in the y-direction;
an inverse Fourier transform module for performing compensation processing on the fourth echo data and then performing k-related processingxAnd kyTo obtain fifth echo data fk(xEyes of a user，yEyes of a user，zEyes of a user)；
An accumulation module for f corresponding to different wave number k values in the fifth echo datak(xEyes of a user，yEyes of a user，zEyes of a user) Accumulating to obtain the scattering coefficient f (x) of the imaging objectEyes of a user，yEyes of a user，zEyes of a user)；
And the output module is used for outputting the scattering coefficient of the imaging object so that the scattering coefficient generates a reconstructed image.
A readable storage medium , having stored thereon a computer program, characterized in that the program, when being executed by a processor, is adapted to carry out the steps of the method of any of claims 1-7 through .
10, imaging device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, wherein the processor when executing the program implements the steps of the method of any of claims 1-7 through .
Technical Field
The invention relates to the technical field of millimeter wave imaging, in particular to interpolation-free three-dimensional active millimeter wave imaging methods and systems, a storage medium and imaging equipment.
Background
In recent years, with the development of economy, passenger flow of various transportation modes is continuously increased, security inspection work of important places such as airports, railway stations and the like is paid great attention by , aiming at the security inspection requirement that public transportation and important places carry hidden contraband articles to human bodies, the conventional technical means (such as metal detection, X-ray detection and the like) have limitations and cannot meet application requirements.
The millimeter wave imaging system can be divided into two types according to whether the imaging system radiates millimeter waves, namely passive millimeter wave (also called passive millimeter wave) imaging and active millimeter wave (also called active millimeter wave) imaging, the passive imaging system utilizes a millimeter wave/terahertz radiometer to detect the thermal radiation distribution of a detected target for imaging, no radiation is caused to a human body, but the imaging resolution ratio is relatively low, the active millimeter wave imaging system emits millimeter wave/terahertz signals with fixed power ( is milliwatt level), and partial echo signals scattered back by the detected target collected by a receiver are utilized for imaging.
The imaging efficiency of the conventional three-dimensional active millimeter wave security inspection imaging method is improved to a certain extent by , but how to further improve the imaging efficiency by is a problem to be solved urgently.
Disclosure of Invention
In view of the above, the present invention has been made to provide methods and systems, storage media, and imaging devices for interpolation-free three-dimensional active millimeter wave imaging that overcome or at least partially address the above-mentioned problems.
, the present application provides the following technical solutions through embodiments of the present application:
A method of interpolation-free three-dimensional active millimeter wave imaging, the method comprising:
acquiring th echo data of an imaging object, wherein the th echo data comprise line-breaking tone signals s (x) corresponding to the imaging object which are acquired at equal intervals on a receiving plane according to preset sampling time intervalsIs connected with，yIs connected withT), wherein the receiving plane and the imaging subject are located in the same three-dimensional coordinate system, the three-dimensional coordinate system including an x-axis, a y-axis, and a z-axis,the receiving plane is Z ═ Z1，(xIs connected with，yIs connected with) Representing the position coordinates of the sampling points on the receiving plane, wherein t is a time domain;
performing phase compensation on the th echo data to obtain second echo data sc(xIs connected with，yIs connected withK); wherein the content of the first and second substances,
based on the reference distance used by the line-off tone modulation signal in the line-off tone modulation process, correcting the second echo data to obtain third echo data sd(xIs connected with，yIs connected with，k)；
Performing two-dimensional fast Fourier transform on the third echo data on the receiving plane to obtain fourth echo data Sd(kx，kyK); wherein k isxDenotes the component of k in the x-direction, kyRepresents the component of k in the y-direction;
after the fourth echo data is compensated, k is related toxAnd kyTo obtain fifth echo data fk(xEyes of a user，yEyes of a user，zEyes of a user)；
F corresponding to different values of wave number k in the fifth echo datak(xEyes of a user，yEyes of a user，zEyes of a user) Accumulating to obtain the scattering coefficient f (x) of the imaging objectEyes of a user，yEyes of a user，zEyes of a user)；
And outputting the scattering coefficient of the imaging object, and enabling the scattering coefficient to generate a reconstructed image.
Optionally, the line-disconnected tone signal specifically includes:
wherein the content of the first and second substances,
Optionally, the phase compensation is performed on the th echo data to obtain second echo data sc(xIs connected with，yIs connected withK), specifically including:
performing Fast Fourier Transform (FFT) on the th echo data in the t dimension to obtain:
S(xis connected with，yIs connected with，ξ)＝FFT[s(xIs connected with，yIs connected with，t)]Wherein ξ denotes frequency;
at dimension ξ, pair S (x)Is connected with，yIs connected withξ) to obtain:
to Sc(xIs connected with，yIs connected withξ) Inverse Fast Fourier Transform (IFFT) in ξ dimensions, resulting in a reduction:
let fd＝fc+γt，
optionally, the second echo data is modified based on a reference distance used by the line-off tone signal in the line-off tone process, so as to obtain third echo data sd(xIs connected with，yIs connected withK), specifically including:
optionally, after performing compensation processing on the fourth echo data, k is performedxAnd kyTo obtain fifth echo data fk(xEyes of a user，yEyes of a user，zEyes of a user) The method specifically comprises the following steps:
wherein k iszRepresenting the component of k in the z-direction,
optionally, two-dimensional fast fourier transform is performed on the third echo data on the receiving plane to obtain fourth echo data Sd(kx，kyK), further comprising:
for different k, the third echo data is simultaneously processed with x in a parallel computing modeIs connected withAnd yIs connected withObtaining fourth echo data S by two-dimensional fast Fourier transformd(kx，ky，k)。
Optionally, after performing compensation processing on the fourth echo data, k is performedxAnd kyTo obtain fifth echo data fk(xEyes of a user，yEyes of a user，zEyes of a user) The method also comprises the following steps:
for different k and zEyes of a userPerforming compensation processing on the fourth echo data and k in parallel computing mannerxAnd kyTo obtain fifth echo data fk(xEyes of a user，yEyes of a user，zEyes of a user)。
In another aspect, the present application provides, via another embodiment of the present application, interpolation-free three-dimensional active millimeter wave imaging system, comprising:
a data acquisition module for acquiring th echo data of an imaging object, wherein the th echo data comprises a demodulation line tone signal s (x) corresponding to the imaging object which is acquired at equal intervals on a receiving plane according to a preset sampling time intervalIs connected with，yIs connected withT), wherein the receiving plane and the imaging subject are located in the same three-dimensional coordinate system, the three-dimensional coordinate system including an x-axis, a y-axis, and a Z-axis, the receiving plane being Z ═ Z1，(xIs connected with，yIs connected with) Representing the position coordinates of the sampling points on the receiving plane, wherein t is a time domain;
a compensation module for performing phase compensation on the th echo data to obtain second echo data sc(xIs connected with，yIs connected withK); wherein the content of the first and second substances,
a correction module, configured to correct the second echo data based on a reference distance used by the line-off tone modulation signal in the line-off tone modulation process, so as to obtain third echo data sd(xIs connected with，yIs connected with，k)；
A Fourier transform module for performing two-dimensional fast Fourier transform on the third echo data on the receiving plane to obtain fourth echo data Sd(kx，kyK); wherein k isxDenotes the component of k in the x-direction, kyRepresents the component of k in the y-direction;
an inverse Fourier transform module for performing compensation processing on the fourth echo data and then performing k-related processingxAnd kyTo obtain fifth echo data fk(xEyes of a user，yEyes of a user，zEyes of a user)；
An accumulation module for f corresponding to the wave number kk(xEyes of a user，yEyes of a user，zEyes of a user) Accumulating to obtain the scattering coefficient f (x) of the imaging objectEyes of a user，yEyes of a user，zEyes of a user)；
And the output module is used for outputting the scattering coefficient of the imaging object so that the scattering coefficient generates a reconstructed image.
The invention discloses readable storage media having stored thereon a computer program which, when executed by a processor, performs the steps of the above method.
The invention discloses imaging devices comprising a memory, a processor and a computer program stored on the memory and executable on the processor, the processor performing the steps of the method.
or more technical solutions provided in the embodiments of the present application have at least the following technical effects or advantages:
the method of the invention firstly acquires th echo data of an imaging object, wherein the th echo data comprises a demodulation line tone signal s (x) scattered by the imaging object and acquired at equal intervals on a receiving plane according to a preset sampling time intervalIs connected with，yIs connected withT), wherein the receiving plane and the imaging subject are located in the same three-dimensional coordinate system, the three-dimensional coordinate system including an x-axis, a y-axis, and a Z-axis, the receiving plane being Z ═ Z1，(xIs connected with，yIs connected with) Representing the position coordinates of the sampling points on the receiving plane, t being the time domain, and then performing phase compensation on the th echo data to obtain second echo data sc(xIs connected with，yIs connected withK); wherein the content of the first and second substances,
Drawings
In order to more clearly illustrate the technical solutions in the embodiments of the present invention, is briefly introduced in the drawings required in the description of the embodiments, it is obvious that the drawings in the following description are embodiments of the present invention, and other drawings can be obtained by those skilled in the art without creative efforts.
FIG. 1 is a flow chart of a method of interpolationless three-dimensional active millimeter wave imaging in embodiments of the present invention;
FIG. 2 is a block diagram of an exemplary interpolationless three-dimensional active millimeter wave imaging system;
FIG. 3 is a schematic view of a receiving plane and a position scene of an imaging subject in embodiments of the invention;
fig. 4 is a comparison of an image generated by the method of embodiments of the invention with an imaged object.
Detailed Description
The embodiment of the application provides interpolation-free three-dimensional active millimeter wave imaging methods and systems, a storage medium and imaging equipment, and solves the technical problem that the imaging efficiency of the active millimeter wave imaging method in the prior art cannot be further improved by steps.
In order to solve the technical problems, the general idea of the embodiment of the application is as follows:
interpolation-free three-dimensional active millimeter wave imaging method comprises the steps of obtaining echo data of an imaging object, performing phase compensation on echo data and obtaining second echo data sc(xIs connected with，yIs connected withK); based on the reference distance used by the line-off tone modulation signal in the line-off tone modulation process, correcting the second echo data to obtain third echo data sd(xIs connected with，yIs connected withK); performing two-dimensional fast Fourier transform on the third echo data on the receiving plane to obtain fourth echo data Sd(kx，kyK); after the fourth echo data is compensated, k is related toxAnd kyTo obtain fifth echo data fk(xEyes of a user，yEyes of a user，zEyes of a user) (ii) a F corresponding to different values of wave number k in the fifth echo datak(xEyes of a user，yEyes of a user，zEyes of a user) Accumulating to obtain the scattering coefficient f (x) of the imaging objectEyes of a user，yEyes of a user，zEyes of a user) (ii) a And outputting the scattering coefficient of the imaging object, and enabling the scattering coefficient to generate a reconstructed image.
In order to better understand the technical solution, the technical solution will be described in detail with reference to the drawings and the specific embodiments.
First, it is noted that the term "and/or" appearing herein only describes kinds of association relations describing association objects, which means that there may be three kinds of relations, for example, a and/or B, which may mean three kinds of relations of a alone, a and B together, and B alone.
The three-dimensional millimeter wave imaging is generally implemented by radiating millimeter waves to an imaging object (e.g., a person) by using a transmitting antenna of an imaging system, and an echo signal returned by part of the imaging object after being scattered is received by a receiving antenna.
Referring to fig. 3, the imaging subject (i.e., the target object) and the receiving plane (i.e., the antenna array scanning plane) are located in the same three-dimensional coordinate system, which includes x-axis, y-axis and Z-axis, and the directions thereof can be arbitrarily adjusted, and only for convenience of calculation, fig. 3 shows cases, i.e., the receiving plane is perpendicular to the Z-axis, and the receiving plane is Z-Z1Assuming that the receiving antenna and the transmitting antenna are at the same positions (actually, the middle point position of the transmitting and receiving antenna is used as the equivalent transmitting and receiving antenna position), referring to fig. 3, the coordinates of the transmitting and receiving antenna are (x)Is connected with，yIs connected with，Z1) The coordinates of the target object are (x)Eyes of a user，yEyes of a user，zEyes of a user)。
The method of the present invention is fully described below in connection with the steps of the present invention as specific embodiments.
Referring to fig. 1, kinds of interpolation-free three-dimensional active millimeter wave imaging methods in the present embodiment include:
s101, acquiring th echo data of an imaging object, whereinSaid th echo data includes line-off tone signals s (x) corresponding to said imaging objects acquired at equal intervals on a receiving plane at preset sampling time intervalsIs connected with，yIs connected withT), wherein the receiving plane and the imaging subject are located in the same three-dimensional coordinate system, the three-dimensional coordinate system including an x-axis, a y-axis, and a Z-axis, the receiving plane being Z ═ Z1，(xIs connected with，yIs connected with) Representing the position coordinates of the sampling points on the receiving plane, wherein t is a time domain;
s102, performing phase compensation on the th echo data to obtain second echo data Sc(xIs connected with，yIs connected withK); wherein the content of the first and second substances,
s103, correcting the second echo data based on the reference distance used by the line-off tone modulation signal in the line-off tone modulation process to obtain third echo data Sd(xIs connected with，yIs connected with，k)；
S104, performing two-dimensional fast Fourier transform on the third echo data on the receiving plane to obtain fourth echo data Sd(kx，kyK); wherein k isxDenotes the component of k in the x-direction, kyRepresents the component of k in the y-direction;
s105, after the fourth echo data are compensated, k is related toxAnd kyTo obtain fifth echo data fk(xEyes of a user，yEyes of a user，zEyes of a user)；
S106, f corresponding to different wave number k values in the fifth echo datak(xEyes of a user，yEyes of a user，zEyes of a user) Accumulating to obtain the scattering coefficient f (x) of the imaging objectEyes of a user，yEyes of a user，zEyes of a user)；
And S107, outputting the scattering coefficient of the imaging object, and enabling the scattering coefficient to generate a reconstructed image.
In a specific implementation process, the echo signals of the imaging object received by the receiving antenna are the accumulation of echo signals of a plurality of point targets in an imaging interval. The transmitted signal is a broadband chirp signal, and the mathematical expression of the complex signal is as follows:
wherein the content of the first and second substances,
fcis the center frequency, gamma is the modulation frequency, c is the speed of light, TpIs the pulse width, j is the unit of the imaginary number,
Then, the receiving antenna is at (x)Is connected with，yIs connected with) The received chirp signal is:
wherein, f (x)Eyes of a user，yEyes of a user，zEyes of a user) For the imaging object in (x)Eyes of a user，yEyes of a user，zEyes of a user) The scattering coefficient of (a) is measured,
Taking the reference signal as:
wherein R isrefA reference distance used by the line-off tone signal in a line-off tone process; t isrefIs the pulse width of the reference signal, greater than TpTo ensure the received signal s within the detection ranger(xIs connected with，yIs connected withT) interval in reference signal sref(t) within the interval.
The reference signal is used for moving the frequency range of the line-breaking tone signal to a proper interval, so that the frequency of the corresponding line-breaking tone signal is relatively lower and is more suitable for sampling.
The imaging system performs dechirping (dechirping) processing on the received broadband linear frequency modulation signal to obtain a corresponding intermediate frequency signal (dechirping signal for short), so that the receiving antenna is positioned on a receiving plane (x)Is connected with，yIs connected with) The received line-disconnected tone signal is:
wherein R isΔ＝R-Rref，RrefThe reference distance used by the line-off tone modulation signal in the line-off tone modulation process ranges from 0 to the maximum measurement distance, and the maximum measurement distance is the distance from the receiving plane to the farthest point of the target object;
In practice, the th echo data are collected as discrete data collected at equal intervals on the receiving plane at predetermined sampling time intervals, i.e., at equal sampling intervals Δ x in the x-direction and Δ y in the y-direction, as required for subsequent fourier transform calculations.
After the th echo data of the imaging object is acquired, the last 1 phase term (i.e., exponential term) in the expression is integrated due to equation (4)
Therefore, as optional embodiments, the phase compensation is performed on the th echo data to obtain the second echo data sc(xIs connected with，yIs connected withK), specifically including:
and performing fast Fourier transform on the th echo data in a t dimension to obtain:
S(xis connected with，yIs connected with，ξ)＝FFT[s(xIs connected with，yIs connected with，t)](5)
Wherein ξ denotes frequency;
at dimension ξ, pair S (x)Is connected with，yIs connected withξ) to obtain:
to Sc(xIs connected with，yIs connected withξ) is subjected to an inverse fast fourier transform in ξ dimensions, resulting in a reduction:
let fd＝fc+γt，
based on the Back Projection (BP) principle, the values at k and z can be obtainedEyes of a userValue of fk(xEyes of a user，yEyes of a user，zEyes of a user) Reconstructing the expression:
wherein the content of the first and second substances,
the exponential term e in the formula (9)j2kRDecomposed as a superposition of plane wave signals (also neglecting the amplitude attenuation coefficient) one can obtain:
wherein k iszThe component representing k in the z direction, i.e., the wavenumber component in the spatial wavenumber domain along the z direction of the coordinate axis, satisfies:
the formula (11) is simplified to the formula (9):
wherein the content of the first and second substances,
F (x) normalized to Eyes of a user，yEyes of a user，zEyes of a user) Corresponding to the gray value of the image, f (x)Eyes of a user，yEyes of a user，zEyes of a user) Namely, the corresponding three-dimensional reconstruction image, the three-dimensional image f (x)Eyes of a user，yEyes of a user，zEyes of a user) The maximum value along the z direction is projected onto the x, y plane, and the projected two-dimensional image g (x, y) can be output.
From the above method principle, it can be seen that f is different for different kk(xEyes of a user，yEyes of a user，zEyes of a user) Can be calculated respectively, so that the parallel calculation mode can be adopted to simultaneously calculate f corresponding to different wave numbers kk(x, y, z), as alternative embodiments, the compensation processing is performed on the fourth echo data, and then k is performedxAnd kyTo obtain fifth echo data fk(xEyes of a user，yEyes of a user，zEyes of a user) The method also comprises the following steps:
for different k and zEyes of a userPerforming compensation processing on the fourth echo data and k in parallel computing mannerxAnd kyTo obtain fifth echo data fk(xEyes of a user，yEyes of a user，zEyes of a user)
Similarly, for different k, the third echo data is simultaneously processed with respect to x by adopting a parallel computing modeIs connected withAnd yIs connected withObtaining fourth echo data S by two-dimensional fast Fourier transformd(kx，ky，k)。
The method can greatly improve the calculation efficiency of the imaging process, reduce the calculation time and obviously improve the imaging efficiency.
The present invention is further illustrated in by specific examples based on the understanding of the principles of the present invention.
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