CN107015466A - The holographic one-point positioning method of optical scanner based on TR MUSIC algorithms - Google Patents
The holographic one-point positioning method of optical scanner based on TR MUSIC algorithms Download PDFInfo
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- G—PHYSICS
- G03—PHOTOGRAPHY; CINEMATOGRAPHY; ANALOGOUS TECHNIQUES USING WAVES OTHER THAN OPTICAL WAVES; ELECTROGRAPHY; HOLOGRAPHY
- G03H—HOLOGRAPHIC PROCESSES OR APPARATUS
- G03H1/00—Holographic processes or apparatus using light, infrared or ultraviolet waves for obtaining holograms or for obtaining an image from them; Details peculiar thereto
- G03H1/22—Processes or apparatus for obtaining an optical image from holograms
- G03H1/2249—Holobject properties
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- G—PHYSICS
- G03—PHOTOGRAPHY; CINEMATOGRAPHY; ANALOGOUS TECHNIQUES USING WAVES OTHER THAN OPTICAL WAVES; ELECTROGRAPHY; HOLOGRAPHY
- G03H—HOLOGRAPHIC PROCESSES OR APPARATUS
- G03H1/00—Holographic processes or apparatus using light, infrared or ultraviolet waves for obtaining holograms or for obtaining an image from them; Details peculiar thereto
- G03H1/22—Processes or apparatus for obtaining an optical image from holograms
- G03H1/2249—Holobject properties
- G03H2001/2252—Location of the holobject
- G03H2001/2255—Holobject out of Fourier or hologram planes
Abstract
The invention discloses the holographic one-point positioning method of the optical scanner based on TR MUSIC algorithms, prior art positioning accurate accuracy is solved not enough, and realize the problem of positioning method is complicated.The present invention, which first changes into laser, scans object after Fresnel single-slit diffraction, obtain the hologram of object and the hologram is obtained into matrix K using Fourier transformation；Then the time reversal matrix of object is obtained by matrix K, and tries to achieve its characteristic value and characteristic vector, so that hologram is decomposed into signal subspace and noise subspace；FInite Element is finally utilized by the equidistant discretization of object, and using unit as trying to achieve unit as hologram during test target after test target, recycle the orthogonality of hologram noise subspace and signal subspace to obtain the imaging puppet spectrum of object, finally give the positional information of detection target.Not only implementation is simple by the present invention, be easy to operation, while having very strong practicality, is adapted to promote the use of.
Description
Technical field
The present invention relates to the holographic one-point positioning method of the optical scanner based on TR-MUSIC algorithms.
Background technology
Optical scanner holographic technique, abbreviation OSH is an important branch of Digital Holography.It utilizes optical scanner
The 3-dimensional information section of object is saved as 2 dimension information by technology, so as to obtain the hologram of object.The technology is, Poon in 1979
Proposed with Korpel when acousto-optic heterodyne image processor is studied.It is holographic aobvious in scanning since being proposed from the technology
The fields such as micro mirror, 3D rendering identification and 3D optical remote sensings are widely used.
Current optical scanner holographic technique implement it is more complicated, and positioning it is accurate on be also short of.
The content of the invention
The technical problem to be solved in the present invention is：There is provided the optical scanner based on TR-MUSIC algorithms holographic One-Point Location side
Method, is realized to the precise positioning of single body, and proposes simultaneously TR-MUSIC is applied in OSH systems to realize to object
The correlation theory of positioning.
To achieve the above object, the technical solution adopted by the present invention is as follows：
The holographic one-point positioning method of optical scanner based on TR-MUSIC algorithms, comprises the following steps：
Step 1, laser using the first polarization beam apparatus is divided into two beams, light beam passes sequentially through the first pupil and afterwards
The second polarization beam apparatus is projected to after one convex lens, the second beam light, which is passed sequentially through, is projected to after the second pupil and the second convex lens
Two polarization beam apparatus, the second polarization beam apparatus interferes to form Fresnel single-slit diffraction by next two-beam optically focused is projected；
The luxuriant and rich with fragrance ripple obtained in step 2, first use step 1 is scanned to object, is then received using photodetector
Transmitted light after scanning, it is demodulated after obtain the section hologram of object, finally hologram is used after Fourier transformation
To matrix K；
Step 3, the time reversal matrix for obtaining by K matrix in step 2 object, and try to achieve its characteristic value and feature to
Amount, so that hologram is decomposed into signal subspace and noise subspace；
Step 4, first with FInite Element by the equidistant discretization of object, and using unit as test target, so
Unit is tried to achieve afterwards as hologram during test target, finally signal subspace using hologram noise subspace and just
The property handed over obtains the imaging puppet spectrum of object, finally gives the positional information of detection target.
Further, the function of first pupil is the function of rectangle 1 in step 1, and the function of the second pupil is dirac δ letters
The focal length of number, the first convex lens and the second convex lens is identical.
Specifically, the optical transfer function of laser is as follows in step 1：
By p1(x, y)=1 and p2(x, y)=δ (x, y) is substituted into formula (1), then formula (1) is expressed as following formula：
The then corresponding space shock response of formula (2) is：
Wherein, j represents imaginary unit* convolution algorithm is represented, the integration that x' and y' represent horizontal and vertical respectively becomes
Amount, x represents the lateral coordinates of object, and y represents the longitudinal coordinate of object, and z represents 2D scanning mirrors to the distance of object under test,Wave number is represented, λ represents optical wavelength, and f represents the focal length of convex lens, kxAnd kyRepresent frequency domain coordinates, p1(x, y) and p2
(x, y) represents the first pupil and the second pupil function respectively.
Specifically, the relational expression that object slice hologram is obtained described in step 2 is as follows：
Wherein, | Γ (x, y；z)|2Represent the complex amplitude function of object, h (x, y；z0) represent scan position in z0Point expand
Dissipate function, F and F-1Fourier transformation and Fourier inversion are represented respectively, and * represents convolution algorithm.
Specifically, the formula that hologram described in step 2 obtains matrix K using Fourier transformation is as follows：
K=F { Hc(x,y；z0)=F | Γ (x, y；z0)|2*h(x,y；z0)} (5)
Wherein, wherein x represents the lateral coordinates of object, and y represents the longitudinal coordinate of object, z0Represent scanning mirror to object
Distance and herein z0For monodrome, Hc(x,y；z0) represent object hologram.
Specifically, the implementation method of step 3 is as follows：
The matrix K tried to achieve in formula (5) is done into singular value decomposition first can obtain time reversal matrix KHK and KKH, specifically such as
Under：
KHK=F-1F (| Γ (x, y；z0)|2)H* h (x, y；-z0) F { h (x, y；z0) * (| Γ (x, y；z0)|2)}}
=F-1F (| Γ (x, y；z0)|2)H* h (x, y；-z0) * h (x, y；z0) * (| Γ (x, y；z0)|2)}}
Wherein, the conjugate transposition computing of H representing matrixs, [h (x, y；z0)]H=h (x, y；-z0), and hologram in OSH
Process of reconstruction be：
|Γ(x,y；z0)|2=(| Γ (x, y；z0)|2)*h(x,y；z0)*h(x,y；-z0) (7)
It therefore, it can obtain time reversal matrix KHK and KKHIt is as follows：
KHK=(| Γ (x, y；z0)|2)H*|Γ(x,y；z0)|2
KKH=| Γ (x, y；z0)|2*(|Γ(x,y；z0)|2)H (8)
Then, time reversal battle array K is tried to achieveHK and KKHEigenvalue λ and characteristic vector v1、v2, the corresponding spy of nonzero eigenvalue
Vector correspondence signal subspace is levied, remaining correspondence noise subspace；From formula (8), v1Carry the feature in object y directions
Information, v2The characteristic information in object x directions is carried, wherein signal subspace and noise subspace is mutually orthogonal, specific as follows：
＜ v1(i=1 ... M), v1(j=M+1 ... N) ＞=0
＜ v2(i=1 ... M), v2(j=M+1 ... N) ＞=0
Wherein, M≤N and M=1, M represent the number of nonzero eigenvalue, and N represents the total number of characteristic value.
Specifically, image objects are obtained using the orthogonality of hologram noise subspace and signal subspace in step 4
The method of puppet spectrum is as follows：
Use v2The hologram K of the conjugate transposition premultiplication test target of the corresponding characteristic vector of middle noise subspacei(Xp) and ask
With Qx(Xp), use v1The corresponding characteristic vector right side of middle noise subspace multiplies the hologram K of test targeti(Xp) and the Q that sumsy
(Xp), i.e.,：
Wherein, XpFor unit test target, and XpFor N × N number of point, Ki(Xp) it is unit test target XpIt is logical
Cross the hologram that formula (4) is tried to achieve, i=1,2,3...N2, m represent vector | Ki(Xp)v1(j)|2Or | v2(j)Ki(Xp)|2M-th yuan
Element, j represents v1Or v (j)2(j) j-th of characteristic vector, M≤N and M=1, M represent the number of nonzero eigenvalue, and N represents feature
The total number of value, Qx(Xp) and Qy(Xp) represent x and y direction test target XpOne median of puppet spectrum.
When test target is detecting the position of target, Qx(Xp) and Qy(Xp) it is approximately equal to 0, and test target is not in detection
During target location, Qx(Xp) and Qy(Xp) value it is limited, try to achieve test target XpQx(Xp) and Qy(Xp) after, you can try to achieve
The x directions of the point and the imaging puppet spectrum P in y directionsxAnd P (Xp)y(Xp), it is specially：
Px(Xp)=| | Ki(Xp)||2/Qx(Xp)
Py(Xp)=| | Ki(Xp)||2/Qy(Xp) (10)
Wherein, Px(Xp) and Py(Xp) represent that the imaging puppet of detection target in the x and y direction is composed respectively, the P in formula (10)x
(Xp) and Py(Xp) test target X can be obtained by being multipliedpImaging puppet spectrum P (Xp), it is specially：
P(Xp)=Px(Xp)Py(Xp) (11)
When P (X are tried to achieve in pointwisep) after, can obtain comprising detection target position information imaging puppet spectrum, eventually through into
As pseudo- spectrum obtains detecting the elaborate position of target.
Specifically, image objects are obtained using the orthogonality of hologram noise subspace and signal subspace in step 4
The method of puppet spectrum is as follows：
First, to test target XpHologram Ki(Xp) do singular value decomposition, that is, try to achieve Ki(Xp) time reversal battle array [Ki
(Xp)]HKi(Xp) and Ki(Xp)[Ki(Xp)]HThe corresponding characteristic vector v of nonzero eigenvalueyAnd vx；
Then, test target X is tried to achieve by following formulapQx(Xp) and Qy(Xp), it is specially：
Wherein, * represents to be conjugated, the transposition computing of T representing matrixs, when test target is detecting the position of target, Qx(Xp)
And Qy(Xp) it is approximately equal to 0, and test target is when detecting target location, Qx(Xp) and Qy(Xp) value it is limited；
Finally, test target X can be tried to achieve by following formulapImaging puppet spectrum P (Xp), visited eventually through the pseudo- spectrum of imaging
The elaborate position of target is surveyed, is specially：
Px(Xp)=| | vx||2/Qx(Xp)
Py(Xp)=| | vy||2/Qy(Xp)
P(Xp)=Px(Xp)Py(Xp) (13)
Wherein Px(Xp) and Py(Xp) the imaging puppet spectrum of detection target in the x and y direction, P (X are represented respectivelyp) represent to include
Detect the imaging puppet spectrum of target position information.
Compared with prior art, the invention has the advantages that：
(1) the initiative use TR-MUSIC algorithms of the present invention are handled hologram, are detected so as to obtain in object
The accurate location of target.
(2) present invention realizes the positioning to detection target using TR-MUSIC algorithms, with higher precision and positioning
Accuracy.
(3) present invention is directed to TR-MUSIC algorithms, is obtained using the orthogonality of object noise subspace and signal subspace
The imaging puppet spectrum of object, gives two kinds of feasible programs, and illustrate the relation of two methods.Give in holoscan technology
Lower use TR-MUSIC algorithms realize the correlation formula of positioning, i.e. formula (1)-formula (13), establish the theoretical foundation of the present invention.
(4) not only implementation is simple, be easy to operation by the present invention, while having very strong practicality, is adapted to promote the use of.
Brief description of the drawings
Fig. 1 is schematic flow sheet of the present invention.
Fig. 2 is the basic block diagram that the embodiment of the present invention is used.
Fig. 3 is the detection target location schematic diagram that the embodiment of the present invention is used.
After Fig. 4 is the singular value decomposition of the embodiment of the present invention, its distribution figure of characterized values.
Fig. 5 is the imaging puppet spectrum that the embodiment of the present invention finally gives.
Embodiment
The invention will be further described with embodiment for explanation below in conjunction with the accompanying drawings, and mode of the invention includes but not only limited
In following examples.
Embodiment
Such as Fig. 1, the holographic one-point positioning method of the optical scanner based on TR-MUSIC algorithms that the present invention is provided, using TR-
MUSIC algorithms are handled hologram, so as to realize the positioning to detecting target, with higher precision and are positioned suitable
Accurately；Not only implementation is simple, be easy to operation, together for the holographic one-point positioning method of this optical scanner based on TR-MUSIC algorithms
When with very strong practicality, be adapted to promote the use of.
The holographic one-point positioning method of this optical scanner based on TR-MUSIC algorithms is using structure as shown in Figure 2 come real
Existing, the structure specifically includes the first polarization beam apparatus BS1, the second polarization beam apparatus BS2, the first pupil p1 (x, y), the second pupil
P2 (x, y), the first convex lens L1, the second convex lens L2, the 3rd convex lens L3, acousto-optic modulator AOFS, the first speculum M1,
Two-mirror M2, scanner X-Y Scanner, photodiode PD, optical-electronic oscillator, two LPF and PC.Laser light
The laser of source transmitting is by being divided into two-beam after the first polarization beam apparatus BS1, wherein light beam passes sequentially through the first speculum, the
One pupil and the first convex lens inject the second polarization beam apparatus BS2, and another light beam passes sequentially through acousto-optic modulator, the second reflection
Mirror, the second pupil and the second convex lens inject the second polarization beam apparatus BS2, and two-beam polymerize by the second polarization beam apparatus BS2
Interference forms Fresnel single-slit diffraction and puts into scanner afterwards, and scanner is by above-mentioned Fresnel single-slit diffraction to testee (Object)
It is scanned, the transmitted light after scanning is by changing into electric signal by photodiode after the 3rd lens and passing through optoelectronic oscillation
Transmitted after device respectively through two LPF to PC.
He-Ne lasers Laser wavelength X=632.8nm in the structure that the present embodiment is used, two convex lens (L1,
L2 focal length) is all 400mm, and the distance of scanning mirror to object is z=400mm, and object is placed as shown in Figure 3, what object was used
Section size is 8mm × 8mm, and object is 16 × 16 through array of the FInite Element after discrete, detection target be placed on coordinate for (10,
5) place.
This optical scanner based on TR-MUSIC algorithms holographic one-point positioning method is concretely comprised the following steps：
Step 1, obtain Fresnel single-slit diffraction.
As shown in Fig. 2 the angular frequency sent by same LASER Light Source is divided into two for ω light by the first polarization beam apparatus BS1
Beam, wherein a branch of pass through the first pupil p1(x, y) formation plane wave；Another beam by acousto-optic modulator produce Ω frequency displacement after again
Pass through the second pupil p2(x, y) formation spherical wave；Two-beam is interfered after polymerizeing through the second polarization beam apparatus BS2 before object under test
Fresnel single-slit diffraction is formed, it can be obtained by formula (3), be specially：
First, the laser that LASER Light Source is sent passes through the first polarization beam apparatus BS1 beam splitting, then respectively through the first pupil p1
(x, y) and the second pupil p2Interference forms Fresnel ripple before object under test after being polymerize after (x, y) by the second polarization beam apparatus
The optical transfer function of band plate is：
The function of the first pupil is the function of rectangle 1 in the present embodiment, and the function of the second pupil is Dirac delta function, and
The first convex lens are provided between the first pupil and the second polarization beam apparatus, are set between the second pupil and the second polarization beam apparatus
There are the second convex lens, and the focal length of the first convex lens and the second convex lens is identical, then, by p1(x, y)=1 and p2(x, y)=δ
(x, y) is substituted into formula (1), then formula (1) is expressed as follows：
The then corresponding space shock response of formula (2) is following formula：
Wherein, x represents the lateral coordinates of object, and y represents the longitudinal coordinate of object, and z represents 2D scanning mirrors to object under test
Distance,Wave number is represented, λ represents optical wavelength, and f represents the focal length of two convex lens, kxAnd kyRepresent frequency domain coordinates,
p1(x, y) and p2(x, y) represents the first pupil and the second pupil function respectively.
Step 2, with Fresnel single-slit diffraction scan object, obtain the hologram of object.
Object is scanned using the Fresnel single-slit diffraction obtained in step 1 first, then connect using photodetector
Transmitted light after being scanned, it is demodulated after obtain the section hologram of object, finally hologram is used after Fourier transformation
Obtain matrix K
To obtain the hologram of object, it can be used：
Again according to the hologram H of objectc(x,y；z0) matrix K is obtained,
K=F { Hc(x,y；z0)=F | Γ (x, y；z0)|2*h(x,y；z0)} (5)
Wherein, x represents the lateral coordinates of object, and y represents the longitudinal coordinate of object, z0Represent scanning mirror to the distance of object
(z herein0For monodrome), Hc(x,y；z0) represent object hologram.
Step 3, the time reversal matrix for obtaining by matrix K object, and its characteristic value and characteristic vector are tried to achieve, so that will
Hologram is decomposed into signal subspace and noise subspace.
First, singular value decomposition is done to matrix K, can be in the hope of matrix K according to formula (5), and then try to achieve time reversal matrix
KHK and KKH, it is specially：
KHK=F-1F (| Γ (x, y；z0)|2)H* h (x, y；-z0) F { h (x, y；z0) * (| Γ (x, y；z0)|2)}}
=F-1F (| Γ (x, y；z0)|2)H* h (x, y；-z0) * h (x, y；Z0) * (| Γ (x, y；z0)|2)}}
Wherein, the conjugate transposition computing of H representing matrixs, [h (x, y；z0)]H=h (x, y；-z0), and hologram in OSH
Process of reconstruction be：
|Γ(x,y；z0)|2=(| Γ (x, y；z0)|2)*h(x,y；z0)*h(x,y；-z0) (7)
It therefore, it can obtain time reversal matrix KHK and KKHIt is as follows：
KHK=(| Γ (x, y；z0)|2)H*|Γ(x,y；z0)|2
KKH=| Γ (x, y；z0)|2*(|Γ(x,y；z0)|2)H (8)
Then, time reversal battle array K is tried to achieveHK and KKHEigenvalue λ and characteristic vector v1、v2, the corresponding spy of nonzero eigenvalue
Vector correspondence signal subspace is levied, remaining correspondence noise subspace, as shown in Figure 4；And from formula (8), v1Carry thing
The characteristic information in body y directions, v2Carry the characteristic information in object x directions.Wherein signal subspace and noise subspace is mutual
It is orthogonal：
＜ v1(i=1 ... M), v1(j=M+1 ... N) ＞=0
＜ v2(i=1 ... M), v2(j=M+1 ... N) ＞=0
Wherein, M (M≤N and herein M=1) represents the number of nonzero eigenvalue, that is to say the number of detection target, and N is represented
The total number of characteristic value.
Step 4, using FInite Element by the equidistant discretization of object, and regard unit as test target；Then ask
Obtain unit and be used as test target Xp(XpFor 16 × 16 points), and can be in the hope of test target X by formula (4)pHologram
Ki(Xp) (i=1,2,3...N2)。
Finally, the imaging puppet for obtaining object using the orthogonality of object noise subspace and signal subspace is composed, such as Fig. 5 institutes
Show, and matched with Fig. 3 article positions placed.In order to obtain the imaging puppet spectrum of object, two kinds of correlations are present embodiments provided
The method of connection, it is specific as follows：
Method 1：Use v2The conjugate transposition premultiplication K of the corresponding characteristic vector of middle noise subspacei(Xp) and the Q that sums to obtainx(Xp),
Use v1The corresponding characteristic vector right side of middle noise subspace multiplies Ki(Xp) and the Q that sumsy(Xp), that is, it is shown below：
When test target is detecting the position of target, Qx(Xp) and Qy(Xp) it is approximately equal to 0, and test target is not in detection
During target location, Qx(Xp) and Qy(Xp) value it is limited.Try to achieve test target XpQx(Xp) and Qy(Xp) after, you can try to achieve this
The x directions of point and the imaging puppet spectrum P in y directionsx(Xp) and Py(Xp) be：
Px(Xp)=| | Ki(Xp)||2/Qx(Xp)
Py(Xp)=| | Ki(Xp)2/Qy(Xp) (10)
Wherein Px(Xp) and Py(Xp) represent that the imaging puppet of detection target in the x and y direction is composed respectively, the P in formula (10)x
(Xp) and Py(Xp) test target X can be obtained by being multipliedpImaging puppet spectrum：
P(Xp)=Px(Xp)Py(Xp) (11)
When P (X are tried to achieve in pointwisep) after, the imaging puppet spectrum comprising detection target position information can be obtained, finally, is passed through
The pseudo- spectrum of imaging obtains detecting the position of target.
Method 2：First, to test target XpHologram Ki(Xp) do singular value decomposition, that is, try to achieve Ki(Xp) time reversal
Battle array [Ki(Xp)]HKi(Xp) and Ki(Xp)[Ki(Xp)]HThe corresponding characteristic vector v of nonzero eigenvalueyAnd vx.Then formula (12) are passed through
Try to achieve test target XpQxAnd Qy, i.e.,：
Wherein, * represents conjugation.When test target is detecting the position of target, Qx(Xp) and Qy(Xp) it is approximately equal to 0, and survey
Target is tried not when detecting target location, Qx(Xp) and Qy(Xp) value it is limited.Finally, test target X can be tried to achieve by following formulap
Imaging puppet spectrum P (Xp), i.e.,：
Px(Xp)=| | vx||2/Qx(Xp)
Py(Xp)=| | vy||2/Qy(Xp)
P(Xp)=Px(Xp)Py(Xp) (13)
Wherein Px(Xp) and Py(Xp) the imaging puppet spectrum of detection target in the x and y direction, P (X are represented respectivelyp) represent to include
Detect the imaging puppet spectrum of target position information.
It is worth noting that, in step 4, object is obtained using the orthogonality of object noise subspace and signal subspace
The two methods of the pseudo- spectrum of imaging be relevant property, make a concrete analysis of as follows：
Process for step 3 and step 4 can be regarded as doing matrix K the process of singular value decomposition, therefore, haveSo as to haveAnd it is correspondingAnd for ＜ v2(j=M+1 ..., N), vx＞ ≈ 0, ＜ v1(j=M+1 ...,
N),vy＞ ≈ 0.Therefore
Wherein C represents constant, and y directions are similarly.Times that a constant is differed between method 1 and method 2 is known from formula (14)
Number relation, and this has no effect on the determination to detecting target location.
The initiative use TR-MUSIC algorithms of the present invention are handled hologram, and detection target is determined so as to realize
Position, with higher precision and position it is quite accurate；Meanwhile, the present invention is directed to TR-MUSIC algorithms, utilizes object noise
The orthogonality of space and signal subspace obtains the imaging puppet spectrum of object, gives two kinds of feasible programs, and illustrate two kinds of sides
The relation of method.And initiative gives the correlation public affairs for realizing positioning using TR-MUSIC algorithms under holoscan technology
Formula, i.e. formula (1)-formula (13), establish the theoretical foundation of the present invention, possess substantive distinguishing features and the marked improvement of protrusion.This hair
Bright not only implementation is simple, simple operation, while having very strong practicality, is adapted to promote the use of.
Above-described embodiment is only one of the preferred embodiment of the present invention, should not be taken to limit the protection model of the present invention
Enclose, as long as the present invention body design thought and mentally make have no the change of essential meaning or polishing, it is solved
Technical problem it is still consistent with the present invention, should be included in protection scope of the present invention within.
Claims (8)
1. the holographic one-point positioning method of the optical scanner based on TR-MUSIC algorithms, it is characterised in that comprise the following steps：
Step 1, laser using the first polarization beam apparatus is divided into two beams, light beam passes sequentially through the first pupil and first convex afterwards
It is projected to the second polarization beam apparatus after lens, the second beam light passes sequentially through that to be projected to second after the second pupil and the second convex lens inclined
Shake beam splitter, and the second polarization beam apparatus interferes to form Fresnel single-slit diffraction by next two-beam optically focused is projected；
The luxuriant and rich with fragrance ripple obtained in step 2, first use step 1 is scanned to object, then receives scanning using photodetector
Transmitted light afterwards, it is demodulated after obtain the section hologram of object, obtain square after hologram finally is used into Fourier transformation
Battle array K；
Step 3, the time reversal matrix for obtaining by K matrix in step 2 object, and its characteristic value and characteristic vector are tried to achieve, from
And hologram is decomposed into signal subspace and noise subspace；
Step 4, first with FInite Element by the equidistant discretization of object, and using unit it is used as test target, Ran Houqiu
Unit is obtained as hologram during test target, the orthogonality of hologram noise subspace and signal subspace is finally utilized
The imaging puppet spectrum of object is obtained, the positional information of detection target is finally given.
2. the holographic one-point positioning method of optical scanner based on TR-MUSIC algorithms according to claim 1, it is characterised in that
The function of first pupil is the function of rectangle 1 in step 1, and the function of the second pupil is Dirac delta function, the first convex lens and second
The focal length of convex lens is identical.
3. the holographic one-point positioning method of optical scanner based on TR-MUSIC algorithms according to claim 2, it is characterised in that
The optical transfer function of laser is as follows in step 1：
By p1(x, y)=1 and p2(x, y)=δ (x, y) is substituted into formula (1), then formula (1) is expressed as following formula：
The then corresponding space shock response of formula (2) is：
Wherein, j represents imaginary unit* convolution algorithm is represented, x' and y' represent horizontal and vertical integration variable, x respectively
The lateral coordinates of object are represented, y represents the longitudinal coordinate of object, and z represents 2D scanning mirrors to the distance of object under test,
Wave number is represented, λ represents optical wavelength, and f represents the focal length of convex lens, kxAnd kyRepresent frequency domain coordinates, p1(x, y) and p2(x, y) point
The first pupil and the second pupil function are not represented.
4. the holographic one-point positioning method of optical scanner based on TR-MUSIC algorithms according to claim 3, it is characterised in that
The relational expression that object slice hologram is obtained described in step 2 is as follows：
Wherein, | Γ (x, y；z)|2Represent the complex amplitude function of object, h (x, y；z0) represent scan position in z0Point spread function
Number, F and F-1Fourier transformation and Fourier inversion are represented respectively, and * represents convolution algorithm.
5. the holographic one-point positioning method of optical scanner based on TR-MUSIC algorithms according to claim 4, it is characterised in that
The formula that hologram described in step 2 obtains matrix K using Fourier transformation is as follows：
K=F { Hc(x,y；z0)=F | Γ (x, y；z0)|2*h(x,y；z0)} (5)
Wherein, wherein x represents the lateral coordinates of object, and y represents the longitudinal coordinate of object, z0Represent scanning mirror to the distance of object
And z herein0For monodrome, Hc(x,y；z0) represent object hologram.
6. the holographic one-point positioning method of optical scanner based on TR-MUSIC algorithms according to claim 5, it is characterised in that
The implementation method of step 3 is as follows：
The matrix K tried to achieve in formula (5) is done into singular value decomposition first can obtain time reversal matrix KHK and KKH, it is specific as follows：
KHK=F-1{F{(|Γ(x,y；z0)|2)H*h(x,y；-z0)}·F{h(x,y；z0)*(|Γ(x,y；z0)|2)}}
=F-1{F{(|Γ(x,y；z0)|2)H*h(x,y；-z0)*h(x,y；z0)*(|Γ(x,y；z0)|2)}}
Wherein, the conjugate transposition computing of H representing matrixs, [h (x, y；z0)]H=h (x, y；-z0), and in OSH hologram weight
The process of building is：
|Γ(x,y；z0)|2=(| Γ (x, y；z0)|2)*h(x,y；z0)*h(x,y；-z0) (7)
It therefore, it can obtain time reversal matrix KHK and KKHIt is as follows：
KHK=(| Γ (x, y；z0)|2)H*|Γ(x,y；z0)|2
KKH=| Γ (x, y；z0)|2*(|Γ(x,y；z0)|2)H (8)
Then, time reversal battle array K is tried to achieveHK and KKHEigenvalue λ and characteristic vector v1、v2, the corresponding feature of nonzero eigenvalue to
Amount correspondence signal subspace, remaining correspondence noise subspace；From formula (8), v1Carry the feature letter in object y directions
Breath, v2The characteristic information in object x directions is carried, wherein signal subspace and noise subspace is mutually orthogonal, specific as follows：
＜ v1(i=1 ... M), v1(j=M+1 ... N) ＞=0
＜ v2(i=1 ... M), v2(j=M+1 ... N) ＞=0
Wherein, M≤N and M=1, M represent the number of nonzero eigenvalue, and N represents the total number of characteristic value.
7. the holographic one-point positioning method of optical scanner based on TR-MUSIC algorithms according to claim 6, it is characterised in that
In step 4 using the orthogonality of hologram noise subspace and signal subspace obtain image objects puppet spectrum method it is as follows：
Use v2The hologram K of the conjugate transposition premultiplication test target of the corresponding characteristic vector of middle noise subspacei(Xp) and sum
Qx(Xp), use v1The corresponding characteristic vector right side of middle noise subspace multiplies the hologram K of test targeti(Xp) and the Q that sumsy(Xp), i.e.,：
Wherein, XpFor unit test target, and XpFor N × N number of point, Ki(Xp) it is unit test target XpPass through formula
(4) hologram tried to achieve, i=1,2,3...N2, m represent vector | Ki(Xp)v1(j)|2Or | v2(j)Ki(Xp)|2M-th of element, j
Represent v1Or v (j)2(j) j-th of characteristic vector, M≤N and M=1, M represent the number of nonzero eigenvalue, and N represents characteristic value
Total number, Qx(Xp) and Qy(Xp) represent x and y direction test target XpOne median of puppet spectrum.
When test target is detecting the position of target, Qx(Xp) and Qy(Xp) it is approximately equal to 0, and test target is not in detection target position
When putting, Qx(Xp) and Qy(Xp) value it is limited, try to achieve test target XpQx(Xp) and Qy(Xp) after, you can try to achieve the x of the point
The imaging puppet spectrum P in direction and y directionsx(Xp) and Py(Xp), it is specially：
Px(Xp)=| | Ki(Xp)||2/Qx(Xp)
Py(Xp)=| | Ki(Xp)||2/Qy(Xp) (10)
Wherein, Px(Xp) and Py(Xp) represent that the imaging puppet of detection target in the x and y direction is composed respectively, the P in formula (10)x(Xp)
And Py(Xp) test target X can be obtained by being multipliedpImaging puppet spectrum P (Xp), it is specially：
P(Xp)=Px(Xp)Py(Xp) (11)
When P (X are tried to achieve in pointwisep) after, the imaging puppet spectrum comprising detection target position information can be obtained, it is pseudo- eventually through imaging
Spectrum obtains detecting the elaborate position of target.
8. the holographic one-point positioning method of the optical scanner based on TR-MUSIC algorithms according to claim 6, its feature exists
In, in step 4 using the orthogonality of hologram noise subspace and signal subspace obtain image objects puppet spectrum method it is as follows：
First, to test target XpHologram Ki(Xp) do singular value decomposition, that is, try to achieve Ki(Xp) time reversal battle array [Ki(Xp)]HKi(Xp) and Ki(Xp)[Ki(Xp)]HThe corresponding characteristic vector v of nonzero eigenvalueyAnd vx；
Then, test target X is tried to achieve by following formulapQx(Xp) and Qy(Xp), it is specially：
Wherein, * represents to be conjugated, the transposition computing of T representing matrixs, when test target is detecting the position of target, Qx(Xp) and Qy
(Xp) it is approximately equal to 0, and test target is when detecting target location, Qx(Xp) and Qy(Xp) value it is limited；
Finally, test target X can be tried to achieve by following formulapImaging puppet spectrum P (Xp), obtain detecting mesh eventually through the pseudo- spectrum of imaging
Target elaborate position, be specially：
Px(Xp)=| | vx||2/Qx(Xp)
Py(Xp)=| | vy||2/Qy(Xp)
P(Xp)=Px(Xp)Py(Xp) (13)
Wherein Px(Xp) and Py(Xp) the imaging puppet spectrum of detection target in the x and y direction, P (X are represented respectivelyp) represent comprising detection
The imaging puppet spectrum of target position information.
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