CN102540183B - Three-dimensional microwave imaging method based on cylinder geometry - Google Patents

Abstract

The invention discloses a three-dimensional microwave imaging method based on cylinder geometry, which relates to the microwave imaging technology. The three-dimensional microwave imaging method includes successively completing two-dimensional imaging on different cylinder surfaces by means of designing focusing functions corresponding to various imaging cylinder surfaces, and finally realizing three-dimensional imaging of a total objective region. The three-dimensional microwave imaging method avoids approximation in a processing process, main operations are carried out in a height wave number field and an orientation wave number field, interpolation is not required in a three-dimensional wave number field, and accordingly accurate and high-efficient three-dimensional imaging can be realized.

Description

Three-dimensional microwave imaging method based on cylinder geometry

Technical field

The present invention relates to the microwave Imaging Technique field, be based on the three-dimensional microwave imaging method of cylinder geometry.

Background technology

The microwave imaging of 360 ° of cylinder scanning geometry can be carried out omnibearing observation to target, and can realize the high resolution three-dimensional imaging to target.In conjunction with the distinctive through characteristic of microwave, be fit to very much be applied to imaging and the detection of low coverage vanishing target based on the microwave means of cylinder scanning how much, for example: target surface three-dimensional imaging, Non-Destructive Testing and target scattering characteristics diagnosis etc.

Accordingly, the microwave imaging method based on this scan geometry is proposed successively.M.Soumekh has proposed a kind of three-dimensional wave number field method (reference: M.Soumekh of decomposing based on tapered plane Green function F ourier, " Reconnaissance with Slant plane Circular SAR Imaging; " IEEE Trans.Image Processing, vol.5, no.8, pp.1252-1265, Aug.1996.), because this method is carried out batch operation at wavenumber domain to target, therefore very high efficient arranged, shortcoming is complicated operation, and the approximate focusing quality that influences image in the method.Method (the reference: Fortuny J. that people such as J.F.Lopez-Sanchez propose, Lopez-Sanchez J.M., Extension of the 3-D range migration algorithm to cylindrical and spherical scanning geometries, " IEEETrans.on Antennas and Propagation; Vol.49; No.10; pp.1434-1444; 2001.); at first by the wave equation decomposition cylinder scanning data are converted to the flat scanning data, use 3DRang Migration Algorithm (RMA) that the flat scanning data are carried out the 3D imaging then.This method operation efficiency is higher, but can only be used for how much of low-angle cylinder scannings.These two kinds of methods are all carried out three-dimensional reconstruction to target under the Cartesian coordinate system.

Though formation method operation efficiency above-mentioned all than higher, all exists approximate, and all need complicated interpolation operation.

Summary of the invention

The objective of the invention is to disclose a kind of three-dimensional microwave imaging method based on cylinder geometry, overcome defective in the prior art, under cylindrical-coordinate system, observed object is carried out three-dimensional reconstruction, realized the quick accurately image of full aperture (360 °), and do not needed interpolation operation.

For achieving the above object, technical solution of the present invention is:

A kind of three-dimensional microwave imaging method based on cylinder geometry, it comprises that step is as follows:

Step S1: original echo is converted into apart from compression domain according to the form that transmits.Be linear FM signal (Chirp signal) if transmit, the echoed signal that obtains is carried out distance to compression, picked up signal S ₁(r, φ ', z '), wherein, r is the metric space territory, φ ' ∈ [0,2 π) be the aerial position position angle, φ ' direction be defined as the orientation to, z ' is the aerial position height, z ' direction be defined as the height to; If transmit to stepping frequency continuous wave signal, the echoed signal that obtains made distance to inverse Fourier transform (IFFT), picked up signal S ₁(r, φ ', z ');

Step S2: to the S as a result of step S1 gained ₁(r, φ ', z ') carries out ripple propagation loss compensation, picked up signal S ₂(r, φ ', z ');

Step S3: to the S as a result of step S2 gained ₂(r, φ ', z ') makes distance to Fourier transform (FFT), picked up signal S ₃(K _ω, φ ', z '), K wherein _ω=2 π f/c are wave number, and f is the transmission frequency of signal, and c is the light velocity;

Step S4: to the S as a result of step S3 gained ₃(K _ω, φ ', z ') and make height to Fourier transform, picked up signal S ₄(K _ω, φ ', K _z), wherein, K _zFor the height to wave number;

Step S5: to the S as a result of step S4 gained ₄(K _ω, φ ', K _z) make the orientation to Fourier transform, picked up signal S ₅(K _ω, K _φ, K _z), wherein, K _φFor the orientation to wave number;

Step S6: to the S as a result of step S5 gained ₅(K _ω, K _φ, K _z) and focus function

Multiply each other picked up signal S ₆(K _ω, K _φ, K _z), wherein, symbol * represents conjugation, ρ _n=n Δ ρ is given imaging face of cylinder radius, n=0, and 1,2 .., (N-1), Δ ρ=c/2B,

The integral part that ρ '/Δ ρ is got in expression;

Step S7: to the S as a result of step S6 gained ₆(K _ω, K _φ, K _z) along K _ωIntegration, picked up signal S ₇(K _φ, K _z);

Step S8: to the S as a result of step S7 gained ₇(K _φ, K _z) do the orientation to the height to two-dimentional inverse Fourier transform (IFFT), the acquisition radius is ρ _nThe face of cylinder on reconstructed image

$\hat{I}({\mathrm{\ρ}}_n,\mathrm{\φ},z)=\underset{K_{\mathrm{\φ}},K_z}{\∫\∫}{S}_7(K_{\mathrm{\φ}},K_z)\exp (j{K}_{\mathrm{\φ}}\mathrm{\φ}+j{K}_{z}z)d{K}_{\mathrm{\φ}}d{K}_z$

Wherein, φ is the position angle, target location, and z is the target location height.

Step S9: finish the reconstruction on all faces of cylinder in the target area, obtain the 3-D view of target area at last;

Step S10: image shows, directly shows image under cylindrical-coordinate system, or by coordinate transform, the image under the cylindrical-coordinate system is transformed to rectangular coordinate system, and (x, y z) show; Its coordinate transformation equation is:

$\left\{\begin{array}{c}x=\mathrm{\ρ}\cos \mathrm{\φ}\\ y=\mathrm{\ρ}\sin \mathrm{\φ}\\ z=z\end{array}\right..$

Wherein, ρ is the target location radius.

Described three-dimensional microwave imaging method, the signal S among its described step S1 ₁(r, φ ', z ') is linear FM signal (Chirp signal) if transmit, and its expression formula is:

$S_1(r,{\mathrm{\φ}}^{\′},z^{\′})=E_c(t,{\mathrm{\φ}}^{\′},z^{\′})\⊗p\left(t\right)$

$~{\&Integral;}_{V}I(\mathrm{\&rho;},\mathrm{\&phi;},z)\sin c[2B(r-R)/c]\exp \{-j2K_{c}R\}/{\mathrm{<figure-callout\; id="2"\; label="R"\; filenames="HDA0000038059310000021.png,HDA0000038059310000061.png"\; state="\{\{state\}\}">R</figure-callout>}}^2\mathrm{dV}$

Wherein, p (t) is the Chirp signal of emission, and t is the fast time, symbol

The expression convolution, symbol ∫ _VDV represents volume integral is carried out in the target area, and B is transmitted signal bandwidth, and r=tc/2 is the metric space territory, K _c=2 π f _cWave number centered by the/c, f _cCentered by frequency, R is the distance that target arrives antenna, expression formula is:

$R=\sqrt{{\mathrm{\&rho;}}^{\&prime;2}+{\mathrm{\&rho;}}^2-2{\mathrm{\&rho;}}^{\&prime;}\mathrm{\&rho;}\cos (\mathrm{\&phi;}-{\mathrm{\&phi;}}^{\&prime;})+{(z-z^{\&prime;})}^2}$

E _c(t, φ ', z ') is the echoed signal under the situation of Chirp signal for transmitting, and its expression formula is:

E _c(t，φ′，z′)＝∫ _VI(ρ，φ，z)p(t-2R/c)dV

If transmit to stepping frequency continuous wave signal, the echoed signal that obtains made distance to inverse Fourier transform (IFFT), picked up signal S ₁(r, φ ', z '):

$S_1(r,{\mathrm{\&phi;}}^{\&prime;},z^{\&prime;})=\underset{K_{\mathrm{\&omega;}}}{\&Integral;}E(K_{\mathrm{\&omega;}},{\mathrm{\&phi;}}^{\&prime;},z^{\&prime;})\exp \left[j2(K_{\mathrm{\&omega;}}-K_c)r\right]d{K}_{\mathrm{\&omega;}}$

$~{\&Integral;}_{V}I(\mathrm{\&rho;},\mathrm{\&phi;},z)\sin c[2B(r-R)/c]\exp \{-j2K_{c}R\}/{\mathrm{<figure-callout\; id="2"\; label="R"\; filenames="HDA0000038059310000021.png,HDA0000038059310000061.png"\; state="\{\{state\}\}">R</figure-callout>}}^2\mathrm{dV}$

Wherein, E (K _ω, φ ', z ') and be the stepping echoed signal under the situation of continuous wave signal frequently for transmitting, its expression formula is:

E(K _ω，φ′，z′)＝∫ _VI(ρ，φ，z)exp(-j2K _ωR)/R ²dV。

Described three-dimensional microwave imaging method, the signal S among its described step S2 ₂(r, φ ', z '), expression formula is:

S ₂(r，φ′，z′)＝H ₁(r)·S ₁(r，φ′，z′)

～∫ _VI(ρ，φ，z)sinc[2B(r-R)/c]exp{-j2K _cR}dV

Wherein, H ₁(r)=r ²Be penalty function.

Described three-dimensional microwave imaging method, the signal S among its described step S3 ₃(K _ω, φ ', z '), expression formula is:

S ₃(K _ω，φ′，z′)＝∫ _VS ₂(r，φ′，z′)exp[-j2(K _ω-K _c)r]dr。

～∫ _VI(ρ，φ，z)exp(-j2K _ωR)dV

Described three-dimensional microwave imaging method, the signal S among its described step S4 ₄(K _ω, φ ', K _z), expression formula is:

S ₄(K _ω，φ′，K _z)＝∫ _rS ₃(r，φ′，z′)exp(-jK _zz′)dz′

～∫ _VI(ρ，φ，z)exp(-jK _zz)g _ρ(K _ω，φ′-φ，K _z)dV

Wherein,

Described three-dimensional microwave imaging method, the signal S among its described step S5 ₅(K _ω, K _φ, K _z), expression formula is:

S ₅(K _ω，K _φ，K _z)＝∫ _rS ₄(r，φ′，z′)exp(-jK _φφ′)dφ′

～∫ _VI(ρ，φ，z)exp(-jK _φφ-jK _zz)G _ρ(K _ω，K _φ，K _z)dV

Wherein, G _ρ(K _ω, K _φ, K _z)=∫ _{φ '}g _ρ(K _ω, φ ', K _z) exp (jK _φφ ') d φ '.

Described three-dimensional microwave imaging method, the signal S among its described step S6 ₆(K _ω, K _φ, K _z), expression formula is:

S ₆(K _ω，K _φ，K _z)＝S ₅(K _ω，K _φ，K _z)·H ₂(K _ω，K _φ，K _z)

～ρ _n|H ₂(K _ω，K _φ，K _z)| ²I(ρ _n，φ，z)exp(-jK _φφ-jK _zz)。

Described three-dimensional microwave imaging method, the signal S among its described step S7 ₆(K _ω, K _φ, K _z), expression formula is:

$S_7(K_{\mathrm{\&phi;}},K_z)=\underset{K_{\mathrm{\&omega;}}}{\&Integral;}{S}_6(K_{\mathrm{\&omega;}},K_{\mathrm{\&phi;}},K_z)d{K}_{\mathrm{\&omega;}}$

$~A(K_{\mathrm{\&phi;}},K_z)I({\mathrm{\&rho;}}_n,\mathrm{\&phi;},z)\exp (-j{K}_{\mathrm{\&phi;}}\mathrm{\&phi;}-j{K}_{z}z)$

Wherein,

Be amplitude function, in microwave imaging, what play a major role is signal phase, and amplitude function does not constitute influence to figure image focu itself, ignores.

Described three-dimensional microwave imaging method, its described focus function H ₂(K _ω, K _φ, K _z) building method adopt numerical method, concrete operations are: at first to given imaging face of cylinder radius ρ _n, generate signal:

$g_{{\mathrm{\&rho;}}_n}(K_{\mathrm{\&omega;}},{\mathrm{\&phi;}}^{\&prime;},K_z)=\exp (-j\sqrt{4K_{\mathrm{\&omega;}}^2-K_z^2}\&CenterDot;\sqrt{{\mathrm{\&rho;}}^{\&prime;2}+{\mathrm{\&rho;}}_n^2-2{\mathrm{\&rho;}}^{\&prime;}{\mathrm{\&rho;}}_{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="HDA0000038059310000021.png,HDA0000038059310000061.png"\; state="\{\{state\}\}">n</figure-callout>}}^2\cos {\mathrm{\&phi;}}^{\&prime;}})$

Right then

Carry out the orientation to Fourier transform (FFT), obtain signal:

$G_{{\mathrm{\&rho;}}_n}(K_{\mathrm{\&omega;}},K_{\mathrm{\&phi;}},K_z)={\&Integral;}_{{\mathrm{\&phi;}}^{\&prime;}}{g}_{{\mathrm{\&rho;}}_n}(K_{\mathrm{\&omega;}},{\mathrm{\&phi;}}^{\&prime;},K_z)\exp (-j{K}_{\mathrm{\&phi;}}{\mathrm{\&phi;}}^{\&prime;})d{\mathrm{\&phi;}}^{\&prime;}$

Focus function H ₂(K _ω, K _φ, K _z) be

Conjugation, that is:

$H_2(K_{\mathrm{\&omega;}},K_{\mathrm{\&phi;}},K_z)={G_{{\mathrm{\&rho;}}_n}}^{*}(K_{\mathrm{\&omega;}},K_{\mathrm{\&phi;}},K_z).$

Described three-dimensional microwave imaging method, its described step S9 comprises step:

Step S91: judge n＜N-1, be, then return step S6, not, then enter step S92;

Step S92: enter step S10.

A kind of three-dimensional microwave imaging method based on cylinder geometry of the present invention, can carry out three-dimensional imaging fast, accurately to the target being observed zone, not approximate in processing procedure, and mainly operate in height wavenumber domain and the orientation wavenumber domain and carry out, therefore need not to carry out interpolation at the three-dimensional wave number field, can realize accurately, three-dimensional imaging efficiently.

Description of drawings

Fig. 1 is of the present invention based on cylinder geometric representation in the three-dimensional microwave imaging method of cylinder geometry;

Fig. 2 is the three-dimensional microwave imaging method step synoptic diagram based on cylinder geometry of the present invention;

Fig. 3 a is the three-dimensional spatial distribution synoptic diagram of 18 * 17 point targets comprising of the emulation of the inventive method embodiment, ordinate be height to, unit be meter (m), horizontal ordinate be the orientation to, unit is radian (rad.);

Fig. 3 b be among Fig. 3 a the two-dimensional projection of target on radius ρ=0.2m face of cylinder show synoptic diagram, ordinate be height to, unit is meter (m), horizontal ordinate be the orientation to, unit is radian (rad.);

Fig. 4 a is three-dimensional imaging result-3dB profile synoptic diagram of the inventive method embodiment, and corresponding to the target among Fig. 3 a, ordinate is that height be rice (m) to, unit, horizontal ordinate be the orientation to, unit is meter (m);

Fig. 4 b is at radius ρ among Fig. 4 a _nTargeted cylindrical perspective view on the=0.2m, ordinate are that height be rice (m) to, unit, horizontal ordinate be the orientation to, unit is meter (m).

Description of symbols in the accompanying drawing:

Antenna array---1; The target area---2;

Embodiment

Below in conjunction with accompanying drawing the three-dimensional microwave imaging method based on cylinder geometry of the present invention is described in detail, be to be noted that described embodiment only is intended to be convenient to the understanding of the present invention, and the present invention is not played any restriction effect.

As shown in Figure 1, under the cylindrical-coordinate system, the dual-mode antenna position be (ρ ', φ ', z '), wherein ρ ' is the radius of cylinder scan aperture, and φ ' ∈ [0,2 π) be the aerial position position angle, φ ' direction be defined as the orientation to, z ' is the aerial position height, z ' direction be defined as the height to.Under cylindrical-coordinate system, the scattering coefficient equation of target area is that (z), wherein ρ is the target location radius to I for ρ, φ, and φ is the position angle, target location, and z is the target location height.

As shown in Figure 2, for the echoed signal that obtains is carried out focal imaging, a kind of three-dimensional microwave imaging method based on cylinder geometry of the present invention comprises that step is as follows:

Step S1: original echo is converted into apart from compression domain according to the form that transmits.

Be linear FM signal (Chirp signal) if transmit, the echoed signal that obtains is carried out distance to compression, picked up signal S ₁(r, φ ', z ').

$S_1(r,{\mathrm{\&phi;}}^{\&prime;},z^{\&prime;})=E_c(t,{\mathrm{\&phi;}}^{\&prime;},z^{\&prime;})\&CircleTimes;p\left(t\right)$

$~{\&Integral;}_{V}I(\mathrm{\&rho;},\mathrm{\&phi;},z)\sin c[2B(r-R)/c]\exp \{-j2K_{c}R\}/{\mathrm{<figure-callout\; id="2"\; label="R"\; filenames="HDA0000038059310000021.png,HDA0000038059310000061.png"\; state="\{\{state\}\}">R</figure-callout>}}^2\mathrm{dV}---\left(1\right)$

Wherein, p (t) is the Chirp signal of emission, and t is the fast time, symbol

The expression convolution, symbol ∫ _VDV represents volume integral is carried out in the target area, and B is transmitted signal bandwidth, and r=tc/2 is the metric space territory, and c is the light velocity, K _c=2 η f _cWave number centered by the/c, f _cCentered by frequency, R is the distance that target arrives antenna, expression formula is

$R=\sqrt{{\mathrm{\&rho;}}^{\&prime;2}+{\mathrm{\&rho;}}^2-2{\mathrm{\&rho;}}^{\&prime;}\mathrm{\&rho;}\cos (\mathrm{\&phi;}-{\mathrm{\&phi;}}^{\&prime;})+{(z-z^{\&prime;})}^2}---\left(2\right)$

E _c(t, φ ', z ') is the echoed signal under the situation of Chirp signal for transmitting, and its expression formula is

E _c(t，φ′，z′)＝∫ _VI(ρ，φ，z)p(t-2R/c)dV (3)

If transmit to stepping frequency continuous wave signal, the echoed signal that obtains made distance to inverse Fourier transform (IFFT), picked up signal S ₁(r, φ ', z ').

$S_1(r,{\mathrm{\&phi;}}^{\&prime;},z^{\&prime;})=\underset{K_{\mathrm{\&omega;}}}{\&Integral;}E(K_{\mathrm{\&omega;}},{\mathrm{\&phi;}}^{\&prime;},z^{\&prime;})\exp \left[j2(K_{\mathrm{\&omega;}}-K_c)r\right]d{K}_{\mathrm{\&omega;}}$

$~{\&Integral;}_{V}I(\mathrm{\&rho;},\mathrm{\&phi;},z)\sin c[2B(r-R)/c]\exp \{-j2K_{c}R\}/{\mathrm{<figure-callout\; id="2"\; label="R"\; filenames="HDA0000038059310000021.png,HDA0000038059310000061.png"\; state="\{\{state\}\}">R</figure-callout>}}^2\mathrm{dV}$

Wherein, E (K _ω, φ ', z ') and be the stepping echoed signal under the situation of continuous wave signal frequently for transmitting, its expression formula is

E(K _ω，φ′，z′)＝∫ _VI(ρ，φ，z)exp(-j2K _ωR)/R ²dV (4)

Wherein, K _ω=2 π f/c are wave number, and f is the transmission frequency of signal.

Step S2: to the S as a result of step S1 gained ₁(r, φ ', z ') carries out ripple propagation loss compensation, picked up signal S ₂(r, φ ', z ').Penalty function is H ₁(r)=r ²

S ₂(r，φ′，z′)＝H ₁(r)·S ₁(r，φ′，z′)

(5)

～∫ _VI(ρ，φ，z)sinc[2B(r-R)/c]exp{-j2K _cR}dV

Step S3: to the S as a result of step S2 gained ₂(r, φ ', z ') makes distance to Fourier transform (FFT), picked up signal S ₃(K _ω, φ ', z ').

S ₃(K _ω，φ′，z′)＝∫ _VS ₂(r，φ′，z′)exp[-j2(K _ω-K _c)r]dr

(6)

～∫ _VI(ρ，φ，z)exp(-j2K _ωR)dV

Step S4: to the S as a result of step S3 gained ₃(K _ω, φ ', z ') and make height to FFT, picked up signal S ₄(K _ω, φ ', K _z), wherein, K _zFor the height to wave number.

S ₄(K _ω，φ′，K _z)＝∫ _VS ₃(r，φ′，z′)exp(-jK _zz′)dz′

(7)

～∫ _VI(ρ，φ，z)exp(-jK _zz)g _ρ(K _ω，φ′-φ，K _z)dV

Wherein,

Step S5: to the S as a result of step S4 gained ₄(K _ω, φ ', K _z) make the orientation to FFT, picked up signal S ₅(K _ω, K _φ, K _z).

S ₅(K _ω，K _φ，K _z)＝∫ _rS ₄(r，φ′，z′)exp(-jK _φφ′)dφ′

(8)

～∫ _VI(ρ，φ，z)exp(-jK _φφ-jK _zz)G _ρ(K _ω，K _φ，K _z)dV

Wherein, G _ρ(K _ω, K _φ, K _z)=∫ _{φ '}g _ρ(K _ω, φ ', K _z) exp (jK _φφ ') d φ ', K _φFor the orientation to wave number.

Step S6: to the S as a result of step S5 gained ₅(K _ω, K _φ, K _z) and focus function

Multiply each other picked up signal S ₆(K _ω, K _φ, K _z), wherein, symbol

* represent conjugation, ρ _n=n Δ ρ is given imaging face of cylinder radius, n=0, and 1,2 .., (N-1), Δ ρ≤c/2B,

The integral part that ρ '/Δ ρ is got in expression.

S ₆(K _ω，K _φ，K _z)＝S ₅(K _ω，K _φ，K _z)·H ₂(K _ω，K _φ，K _z)

～ρ _n|H ₂(K _ω，K _φ，K _z)| ²I(ρ _n，φ，z)exp(-jK _φφ-jK _zz) (9)

Described focus function H ₂(K _ω, K _φ, K _z) building method can adopt numerical method, concrete operations are: at first to given imaging face of cylinder radius ρ _n, generate signal

$g_{{\mathrm{\&rho;}}_n}(K_{\mathrm{\&omega;}},{\mathrm{\&phi;}}^{\&prime;},K_z)=\exp (-j\sqrt{4K_{\mathrm{\&omega;}}^2-{\mathrm{<figure-callout\; id="2"\; label="K\; z"\; filenames="HDA0000038059310000021.png,HDA0000038059310000061.png"\; state="\{\{state\}\}">K</figure-callout>}}_z^{}}\&CenterDot;\sqrt{{\mathrm{\&rho;}}^{\&prime;2}+{\mathrm{\&rho;}}_n^2-2{\mathrm{\&rho;}}^{\&prime;}{\mathrm{\&rho;}}_{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="HDA0000038059310000021.png,HDA0000038059310000061.png"\; state="\{\{state\}\}">n</figure-callout>}}^2\cos {\mathrm{\&phi;}}^{\&prime;}})---\left(10\right)$

Right then

Carry out the orientation to FFT, obtain signal

$G_{{\mathrm{\&rho;}}_n}(K_{\mathrm{\&omega;}},K_{\mathrm{\&phi;}},K_z)={\&Integral;}_{{\mathrm{\&phi;}}^{\&prime;}}{g}_{{\mathrm{\&rho;}}_n}(K_{\mathrm{\&omega;}},{\mathrm{\&phi;}}^{\&prime;},K_z)\exp (-j{K}_{\mathrm{\&phi;}}{\mathrm{\&phi;}}^{\&prime;})d{\mathrm{\&phi;}}^{\&prime;}---\left(11\right)$

Focus function H ₂(K _ω, K _φ, K _z) be Conjugation, namely

$H_2(K_{\mathrm{\&omega;}},K_{\mathrm{\&phi;}},K_z)={G_{{\mathrm{\&rho;}}_n}}^{*}(K_{\mathrm{\&omega;}},K_{\mathrm{\&phi;}},K_z)---\left(12\right)$

Step S7: to the S as a result of step S6 gained ₆(K _ω, K _φ, K _z) along K _ωIntegration, picked up signal S ₇(K _φ, K _z).

$S_7(K_{\mathrm{\&phi;}},K_z)=\underset{K_{\mathrm{\&omega;}}}{\&Integral;}{S}_6(K_{\mathrm{\&omega;}},K_{\mathrm{\&phi;}},K_z)d{K}_{\mathrm{\&omega;}}---\left(13\right)$

$~A(K_{\mathrm{\&phi;}},K_z)I({\mathrm{\&rho;}}_n,\mathrm{\&phi;},z)\exp (-j{K}_{\mathrm{\&phi;}}\mathrm{\&phi;}-j{K}_{z}z)$

Wherein,

Be amplitude function, in microwave imaging, what play a major role is signal phase, and amplitude function does not constitute influence to figure image focu itself, can ignore.

Step S8: to the S as a result of step S7 gained ₇(K _φ, K _z) do the orientation to the height to two-dimentional IFFT, the acquisition radius is ρ _nThe face of cylinder on reconstructed image

$\hat{I}({\mathrm{\&rho;}}_n,\mathrm{\&phi;},z)=\underset{K_{\mathrm{\&phi;}},K_z}{\&Integral;\&Integral;}{S}_7(K_{\mathrm{\&phi;}},K_z)\exp (j{K}_{\mathrm{\&phi;}}\mathrm{\&phi;}+j{K}_{z}z)d{K}_{\mathrm{\&phi;}}d{K}_z---\left(14\right)$

Step S9: finish the reconstruction on all faces of cylinder in the target area, obtain the 3-D view of target area at last.Step S9 comprises following substep:

Step S91: judge n＜N-1, be, then return step S6, not, then enter step S92.This step can realize by parallel computation, and the N step computing that needs double counting is decomposed into M, and (M≤N) individual thread or process accelerate to realize parallel computation by DSP, FPGA or GPU.

Step S92: enter step S10.

Step S10: image shows.Can directly under cylindrical-coordinate system, show image, also can be by coordinate transform, the image under the cylindrical-coordinate system is transformed to rectangular coordinate system, and (x, y z) show.Coordinate transformation equation is:

$\left\{\begin{array}{c}x=\mathrm{\&rho;}\cos \mathrm{\&phi;}\\ y=\mathrm{\&rho;}\sin \mathrm{\&phi;}\\ z=z\end{array}\right.---\left(15\right)$

Further the inventive method is described below by l-G simulation test, 18 * 17 scattering points are evenly distributed on the face of cylinder that radius is 0.2m in the emulation, and the orientation to angle intervals and the height be respectively 20 ° and 0.10m to the interval, shown in Fig. 3 a.Fig. 3 b has provided the two-dimensional projection demonstration of target on radius ρ=0.2m face of cylinder among Fig. 3 a.Suppose the scattering coefficient unanimity of all targets, the radius ρ '=1.5m of cylinder scan aperture, transmit and be stepping frequency continuous wave signal, operating frequency range is 35GHz～40GHz, frequency sampling interval delta f=50MHz, the orientation is to angle sampling interval Δ φ '=0.358 °, and elevation is to sampling interval Δ z '=0.600cm.

At first, execution in step S1 is to step S5, then according to following formula

$H_2(K_{\mathrm{\&omega;}},K_{\mathrm{\&phi;}},K_z)=G_{{\mathrm{\&rho;}}_n}^{*}(K_{\mathrm{\&omega;}},K_{\mathrm{\&phi;}},K_z)={\left[{\&Integral;}_{{\mathrm{\&phi;}}^{\&prime;}}{g}_{{\mathrm{\&rho;}}_n}(K_{\mathrm{\&omega;}},{\mathrm{\&phi;}}^{\&prime;},K_z)\exp (-j{K}_{\mathrm{\&phi;}}{\mathrm{\&phi;}}^{\&prime;})d{\mathrm{\&phi;}}^{\&prime;}\right]}^{*}---\left(16\right)$

Calculate different radii ρ _nOn focus function H ₂(K _ω, K _φ, K _z), and to the S as a result of step S6 gained ₆(K _ω, K _φ, K _z) along K _ωIntegration is carried out subsequent step S6 to S10 successively, obtains the three-dimensional microwave image of target in the three dimensions, corresponding imaging results as shown in Figure 4, wherein Fig. 4 a be Fig. 3 a target-the 3dB profile diagram, Fig. 4 b is radius ρ among Fig. 4 a _nTargeted cylindrical perspective view on the=0.2m.Can see, adopt the resultant three-dimensional microwave image of the inventive method to coincide with the actual target locations relation, and can tell the space layout of target.

The above; only be the embodiment among the present invention; protection scope of the present invention is not limited thereto; anyly be familiar with the people of this technology in the disclosed technical scope of the present invention; can understand conversion or the replacement expected; all should contain of the present invention comprising within the scope, so protection scope of the present invention should be as the criterion with the protection domain of claims.

Claims (1)

1. the three-dimensional microwave imaging method based on cylinder geometry is characterized in that, comprises that step is as follows:

Step S1: according to the form that transmits original echo being converted into apart from compression domain, is linear FM signal if transmit, and the echoed signal that obtains is carried out distance to compression, picked up signal S ₁(r, φ ', z '), wherein, r is the metric space territory, φ ' ∈ [0,2 π) be the aerial position position angle, φ ' direction be defined as the orientation to, z ' is the aerial position height, z ' direction be defined as the height to; If transmit to stepping frequency continuous wave signal, the echoed signal that obtains made distance to inverse Fourier transform, picked up signal S ₁(r, φ ', z ');

Step S2: to the S as a result of step S1 gained ₁(r, φ ', z ') carries out ripple propagation loss compensation, picked up signal S ₂(r, φ ', z ');

Step S3: to the S as a result of step S2 gained ₂(r, φ ', z ') makes distance to Fourier transform, picked up signal S ₃(K _ω, φ ', z '), K wherein _ω=2 π f/c are wave number, and f is the transmission frequency of signal, and c is the light velocity;

Step S4: to the S as a result of step S3 gained ₃(K _ω, φ ', z ') and make height to Fourier transform, picked up signal S ₄(K _ω, φ ', K _z), wherein, K _zFor the height to wave number;

Step S5: to the S as a result of step S4 gained ₄(K _ω, φ ', K _z) make the orientation to Fourier transform, picked up signal S ₅(K _ω, K _φ, K _z), wherein, K _φFor the orientation to wave number;

Step S6: to the S as a result of step S5 gained ₅(K _ω, K _φ, K _z) and focus function

Multiply each other picked up signal S ₆(K _ω, K _φ, K _z), wherein, symbol * represents conjugation, ρ _n=n Δ ρ is given imaging face of cylinder radius, n=0, and 1,2 .., (N-1), Δ ρ=c/2B,

The integral part that ρ '/Δ ρ is got in expression, B is transmitted signal bandwidth, and ρ ' is the radius of cylinder scan aperture, and ρ is the target location radius, ρ _nBe given imaging face of cylinder radius;

Step S7: to the S as a result of step S6 gained ₆(K _ω, K _φ, K _z) along K _ωIntegration, picked up signal S ₇(K _φ, K _z);

Step S8: to the S as a result of step S7 gained ₇(K _φ, K _z) do the orientation to the height to two-dimentional inverse Fourier transform, the acquisition radius is ρ _nThe face of cylinder on reconstructed image

$\hat{I}({\mathrm{\&rho;}}_n,\mathrm{\&phi;},z)=\underset{K_{\mathrm{\&phi;}},K_z}{\&Integral;\&Integral;}{S}_7(K_{\mathrm{\&phi;}},K_z)\exp ({\mathrm{jK}}_{\mathrm{\&phi;}}\mathrm{\&phi;}+{\mathrm{jK}}_{z}z){\mathrm{dK}}_{\mathrm{\&phi;}}{\mathrm{dK}}_z$

Wherein, φ is the position angle, target location, and z is the target location height;

Step S9: finish the reconstruction on all faces of cylinder in the target area, obtain the 3-D view of target area at last;

Step S10: image shows, directly shows image under cylindrical-coordinate system, or by coordinate transform, the image under the cylindrical-coordinate system is transformed to rectangular coordinate system, and (x, y z) show; Its coordinate transformation equation is:

$\left\{\begin{array}{c}x=\mathrm{\&rho;}\cos \mathrm{\&phi;}\\ y=\mathrm{\&rho;}\sin \mathrm{\&phi;}\\ z=z\end{array}\right.$

Wherein, ρ is the target location radius;

Wherein, focus function H described in the step S6 ₂(K _ω, K _φ, K _z) building method adopt numerical method, concrete operations are: at first to given imaging face of cylinder radius ρ _n, generate signal:

$g_{{\mathrm{\&rho;}}_n}(K_{\mathrm{\&omega;}},{\mathrm{\&phi;}}^{\&prime;},K_z)=\exp (-j\sqrt{{4K}_{\mathrm{\&omega;}}^2-K_z^2}\&CenterDot;\sqrt{{\mathrm{\&rho;}}^{\&prime;2}+{\mathrm{\&rho;}}_n^2-2{\mathrm{\&rho;}}^{\&prime;}{\mathrm{\&rho;}}_n^2\cos {\mathrm{\&phi;}}^{\&prime;}})$

Right then

Carry out the orientation to Fourier transform, obtain signal:

$G_{{\mathrm{\&rho;}}_n}(K_{\mathrm{\&omega;}},K_{\mathrm{\&phi;}},K_z)={\&Integral;}_{{\mathrm{\&phi;}}^{\&prime;}}{g}_{{\mathrm{\&rho;}}_n}(K_{\mathrm{\&omega;}},{\mathrm{\&phi;}}^{\&prime;},K_z)\exp (-j{K}_{\mathrm{\&phi;}}{\mathrm{\&phi;}}^{\&prime;})d{\mathrm{\&phi;}}^{\&prime;}$

Focus function H ₂(K _ω, K _φ, K _z) be

Conjugation, that is:

$H_2(K_{\mathrm{\&omega;}},K_{\mathrm{\&phi;}},K_z)={G_{{\mathrm{\&rho;}}_n}}^{*}(K_{\mathrm{\&omega;}},K_{\mathrm{\&phi;}},K_z)..$

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