CN114675443A - Fractional order modeling method for light beam deflection system based on liquid crystal phased array - Google Patents
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- G—PHYSICS
- G02—OPTICS
- G02F—OPTICAL DEVICES OR ARRANGEMENTS FOR THE CONTROL OF LIGHT BY MODIFICATION OF THE OPTICAL PROPERTIES OF THE MEDIA OF THE ELEMENTS INVOLVED THEREIN; NON-LINEAR OPTICS; FREQUENCY-CHANGING OF LIGHT; OPTICAL LOGIC ELEMENTS; OPTICAL ANALOGUE/DIGITAL CONVERTERS
- G02F1/00—Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics
- G02F1/01—Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics for the control of the intensity, phase, polarisation or colour
- G02F1/13—Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics for the control of the intensity, phase, polarisation or colour based on liquid crystals, e.g. single liquid crystal display cells
- G02F1/133—Constructional arrangements; Operation of liquid crystal cells; Circuit arrangements
- G02F1/13306—Circuit arrangements or driving methods for the control of single liquid crystal cells
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- G02F—OPTICAL DEVICES OR ARRANGEMENTS FOR THE CONTROL OF LIGHT BY MODIFICATION OF THE OPTICAL PROPERTIES OF THE MEDIA OF THE ELEMENTS INVOLVED THEREIN; NON-LINEAR OPTICS; FREQUENCY-CHANGING OF LIGHT; OPTICAL LOGIC ELEMENTS; OPTICAL ANALOGUE/DIGITAL CONVERTERS
- G02F1/00—Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics
- G02F1/29—Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics for the control of the position or the direction of light beams, i.e. deflection
- G02F1/292—Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics for the control of the position or the direction of light beams, i.e. deflection by controlled diffraction or phased-array beam steering
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Abstract
The invention discloses a fractional order modeling method of a beam deflection system based on a liquid crystal phased array. The method comprises the following steps: firstly, an integral order constitutive equation of liquid crystal molecules is rewritten into a fractional order constitutive equation, then, distribution of liquid crystal molecule director under the action of electric field force is described by utilizing a Gibbs free energy equation, and the fractional order constitutive equation of the liquid crystal molecules in the liquid crystal phased array is established by a numerical averaging method. Secondly, a linear fitting method is adopted to obtain the corresponding relation among the phase difference of the liquid crystal phased array, the driving voltage and the inclination angle of liquid crystal molecules. And finally, establishing a fractional order model of the liquid crystal phased array light beam deflection system by combining a liquid crystal phased array light beam regulation and control mechanism, and identifying parameters of the fractional order model by adopting a Legendre wavelet integral operation matrix method. The method can accurately represent the dynamic change process of the light beam, can be used for the research of the liquid crystal phased array light beam deflection control strategy, and realizes the rapid, accurate and stable pointing of the light beam.
Description
Technical Field
The invention belongs to the field of liquid crystal optoelectronic devices, and mainly relates to a fractional order modeling method of a beam deflection system based on a liquid crystal phased array.
Background
In the laser phased array radar, a liquid crystal phased array is a core device for beam scanning, and the beam pointing accuracy and the scanning speed directly influence the radar detection performance. The higher the light beam pointing accuracy is, the more accurate the target positioning is; the faster the scanning speed, the higher the imaging efficiency. Therefore, the rapid and accurate light beam deflection can realize the effective detection of the target, and the accurate liquid crystal phased array light beam deflection model is the key for realizing the rapid and accurate control of the light beam.
At present, researches on modeling of a liquid crystal phased array beam deflection system are mainly divided into two types:
one is mechanism modeling, on one hand, relaxation characteristics of liquid crystal molecules are analyzed, an Erickson-Leslie equation is solved by using a numerical analysis method, a mathematical model between response time and voltage of the liquid crystal molecules is obtained, or an exponential function approximate fitting method is adopted to describe relaxation and relaxation phenomena of the liquid crystal molecules. However, this method only describes the dynamic response process of liquid crystal molecules under the action of an electric field, and a dynamic model between the phase modulation amount of the liquid crystal phased array and the deflection angle of the light beam is not obtained. On the other hand, a wave control model of the light beam deflection system is established based on a radar phased array principle and combined with a kirchhoff diffraction theory, but the method can only obtain the corresponding relation between the deflection angle and the phase modulation amount of the light beam in a steady state, and cannot represent the dynamic change process of the deflection angle of the light beam.
The other type is a system identification method, a high-speed CCD camera is used for collecting miss distance of a light beam centroid, an integral order model of a light beam deflection system phase delay amount and a light beam deflection angle is established by adopting a first-order inertia link, and model parameters are estimated by combining a two-point method.
In summary, no dynamic model capable of accurately representing the phase delay amount and the beam deflection angle of the liquid crystal phased array beam deflection system exists at present.
Disclosure of Invention
The invention provides a fractional order modeling method for a light beam deflection system based on a liquid crystal phased array, which aims to solve the problem that the prior art cannot accurately represent the dynamic response process of liquid crystal phased array light beam deflection.
In order to achieve the above object, the present invention provides a fractional order modeling method for a beam deflection system based on a liquid crystal phased array, comprising the following steps:
the method comprises the following steps: analyzing the stress deformation type of liquid crystal molecules in the liquid crystal phased array, and constructing a fractional order constitutive equation aiming at the deformation characteristic of the liquid crystal molecules under the action of an electric field
Wherein F (t) is the electric field force, η1,η2The viscosity coefficients for splay and bend, respectively. k is a radical of1＝1.11×10-11N is the coefficient of elasticity, k, of splay2＝1.71×10-11And N is the bending elastic coefficient. θ (t) is the tilt angle of the liquid crystal director along the z-axis direction;
step two: describing the distribution of liquid crystal molecular director under the action of electric field force by Gibbs free energy equation, and establishing fractional order constitutive equation of liquid crystal molecules in liquid crystal phased array by numerical averaging method
Where u (t) is the applied drive voltage, q is 1.6 × 10-19C is the electric quantity of unit charge, j is the distribution charge coefficient of liquid crystal molecular body, and x is 9.8 μm, which is the thickness of the liquid crystal layer;
step three: the corresponding relation between the phase difference and the driving voltage of the liquid crystal phased array, the driving voltage and the inclination angle of liquid crystal molecules is obtained by adopting a linear fitting method
Wherein, L is a proportionality coefficient,
is the average value of the tilt angles of the liquid crystal molecules;
step four: substituting the formula (3) and the formula (4) into the formula (2), and establishing a fractional order model of the liquid crystal phased array light beam deflection system by combining a liquid crystal phased array light beam regulation mechanism;
step five: and identifying unknown parameters and fractional orders of the fractional order model of the liquid crystal phased array beam deflection system by adopting a Legendre wavelet integral operation matrix method.
In the first step, the formula (1) is obtained by the following method:
the combination of an elastic element and a viscous element representing the viscoelasticity of the material, the elastic element obeying Hooke's law
σ(t)＝Hφ(t) (6)
Where σ (t) is stress, φ (t) is strain, and H is elastic coefficient.
The viscous element is represented as
σ(t)＝KDαφ(t) (7)
Wherein K is a viscosity coefficient. DαAlpha is the fractional order, which is a fractional order differential operator.
For a single liquid crystal molecule, the deformation process under the action of the electric field force f (t) can be described by the elastic element and the viscous element in parallel. Fractional order viscous element for splay viscous behavior
Denotes that the elasticity is given by k1And theta (t). Similarly, the viscosity of the bend is expressed as
Elasticity of bending is k2θ(t)。η1,η2The viscosity coefficients for splay and bend, respectively. k is a radical of formula1＝1.11×10-11N is the coefficient of elasticity, k, of splay2＝1.71×10-11And N is the bending elastic coefficient. θ (t) is the tilt angle of the liquid crystal director along the z-axis direction. Thus, we can obtain the constitutive equation of a single liquid crystal molecule as
In the second step, the formula (2) is obtained by the following method:
the voltage and the tilt angle of the director of the liquid crystal molecules can be approximated to be linear relation
The average value of the tilt angle of the liquid crystal molecules, the average value of the electric field force, assuming a uniform electric field, is the value of
Wherein q is 1.6 × 10-19C is the electric quantity of unit charge, j is the coefficient of charge distribution of liquid crystal molecular body, and x is 9.8 μm, which is the thickness of liquid crystal layer. Will be given by equations (8) and
substituting into formula (1), we can obtain the fractional order constitutive equation of liquid crystal
The concrete method of the fourth step is as follows: substituting the linear function corresponding to the voltage of 0-3v in the formula (4) obtained in the step three into the formula (3), the relation between the phase modulation amount and the liquid crystal molecule inclination angle average value can be obtained
By substituting the formula (9) into the formula (8), we can obtain the relationship between the beam deflection angle and the tilt angle of the liquid crystal molecules
Substituting the formulas (3) and (10) into the formula (2), we can obtain a fractional order model of the liquid crystal phased array beam deflection angle and the loaded phase delay amount.
Substituting the total delay tau of the system into the formula (11) can finally obtain a fractional order model of the beam deflection system of the liquid crystal phased array as
Compared with the prior art, the invention has the following beneficial effects:
1. the deformation characteristic of the liquid crystal molecules under the action of the electric field force is described by using the memorability and the historical dependence of the fractional calculus, the integral order constitutive equation of the liquid crystal molecules is rewritten into the fractional order constitutive equation, and the established fractional order constitutive equation of the liquid crystal molecules can accurately represent the deformation process of the liquid crystal molecules under the action of the electric field force.
2. The invention establishes the relation between the phase difference of the liquid crystal phased array, the voltage and the inclination angle of liquid crystal molecules by utilizing a linear fitting technology, constructs a fractional order model of a liquid crystal phased array beam deflection system according to the liquid crystal phased array beam deflection principle, and identifies unknown parameters and model orders in the fractional order model by adopting a Legendre wavelet integral operation matrix method, and the established fractional order model can accurately represent the dynamic change process of the beams.
3. The fractional order model established by the invention can be used for researching a liquid crystal phased array beam deflection control strategy and realizing rapid, accurate and stable pointing of the beam.
Drawings
FIG. 1 is a flow chart of a fractional order modeling method of a beam deflection system based on a liquid crystal phased array;
FIG. 2 is a fractional order viscoelastic element; wherein a is an elastic element; b is an adhesive element;
FIG. 3 is a schematic diagram of liquid crystal phased array beam steering;
FIG. 4 is a graph comparing the fitting effect of a fractional order model and an integer order model.
Detailed Description
The present invention will be described in further detail with reference to the following embodiments and the accompanying drawings. The specific embodiments of the present invention and the description thereof are provided for the purpose of illustrating the invention and are not to be construed as limiting the invention.
As shown in fig. 1, the method for calculating the diffraction efficiency of a cascaded liquid crystal polarization grating provided by the present invention includes the following steps:
the method comprises the following steps: liquid crystals are a special material between solid and liquid. And has both the elastic properties of a solid and the viscous properties of a liquid. In the liquid crystal phased array, when no driving voltage is applied, liquid crystal molecules are arranged parallel to the glass substrate, and under the action of the driving voltage, the liquid crystal molecules are subjected to splay and bending deformation. The deformation of the liquid crystal is manifested as the tilt of the director of the liquid crystal molecules in the Z-axis direction under the influence of an electric field force. When the external field voltage is removed, the liquid crystal molecules are restored to the initial state from the current tilt position.
The conventional integral order constitutive equation of liquid crystal molecules is shown as follows
Wherein k is a splay deformation coefficient, E is an electric field, Delta epsilon is the anisotropy of the liquid crystal, and theta is the inclination angle of liquid crystal molecules.
As can be seen from equation (5), the integral order constitutive equation of the liquid crystal molecules is related only to the current time t. However, due to the influence of the viscoelasticity of the liquid crystal molecules, the deformation at the current moment cannot accurately represent the whole deformation process of the liquid crystal molecules in the electric field force. The fractional calculus has history dependence and memory, can accurately describe the whole deformation process of liquid crystal molecules, and in the fractional calculus theory, an elastic element and a viscous element can be used for respectively describing the elasticity and viscosity of the material.
As shown in fig. 2. The viscoelasticity of the material can be expressed by the combination of the two elements. The elastic element obeys Hooke's law
σ(t)＝Hφ(t) (6)
Where σ (t) is stress, φ (t) is strain, and H is elastic coefficient.
The adhesive member may be represented as
σ(t)＝KDαφ(t) (7)
Wherein K is the viscosity coefficient. DαAlpha is the fractional order, which is a fractional order differential operator.
For a single liquid crystal molecule, the deformation process under the action of the electric field force f (t) can be described by the elastic element and the viscous element in parallel. Fractional order viscous element for splay viscous behavior
Denotes that the elasticity is given by k1And theta (t). Similarly, the viscosity of the bend is expressed as
Elasticity of bending is k2θ(t)。η1,η2The viscosity coefficients for splay and bend, respectively. k is a radical of1＝1.11×10-11N is the coefficient of elasticity, k, of splay2＝1.71×10-11And N is the bending elastic coefficient. θ (t) is the tilt angle of the liquid crystal director along the z-axis direction. Thus, we can obtain the constitutive equation of a single liquid crystal molecule as
Step two: according to the theory of elastic deformation of the liquid crystal continuum, the inclination angle of the liquid crystal molecules is related to the position and voltage in the liquid crystal layer. The arrangement of liquid crystal molecules in the liquid crystal phased array presents nonlinearity, and according to the linear fractional order viscoelasticity theory, the voltage and the inclination angle of the director of the liquid crystal molecules can be approximately in a linear relation, so that the voltage and the inclination angle of the director of the liquid crystal molecules are taken
Is an average value of the tilt angle of the liquid crystal molecules.
Due to the fact that
The average value of the tilt angle of the liquid crystal molecules and hence the electric field force is also the average value, and if in a uniform electric field, there is a moment that
Wherein q is 1.6 × 10-19C is the electric quantity of unit charge, j is the coefficient of charge distribution of liquid crystal molecular body, and x is 9.8 μm, which is the thickness of the liquid crystal layer. Will be given by equations (8) and
substituting into formula (1), we can obtain the fractional order constitutive equation of liquid crystal
Step three: the liquid crystal phased array generates a constant phase difference delta phi by adjusting voltage distribution between adjacent electrodes, forms a wave front with the phase modulation amount of 2 phi, calculates driving voltage corresponding to the wave front according to a liquid crystal phase modulation characteristic curve, and then generates a gray scale image and loads the gray scale image on a liquid crystal phased array electrode. Under the action of driving voltage, liquid crystal molecules tilt along the Z-axis direction to perform phase modulation on incident beams, so that deflection of the beams is realized. The beam steering principle is shown in fig. 3.
According to the principle of the phased array radar, the deflection angle theta of the outgoing light beam of the light beam which is normally incident to the liquid crystal phased arraypComprises the following steps:
in order to form a constant phase difference, adjacent electrodes need to apply different driving voltages. The larger the driving voltage, the faster the response speed of the liquid crystal molecules. The deflection of the light beam needs a plurality of electrodes to act together to realize the phase modulation amount of 2 pi. Therefore, to ensure that the beam can be deflected, the minimum drive voltage is the system input.
For better understanding the relationship between the minimum voltage and the phase modulation amount, the phase modulation amount is assumed to be
5 electrodes are required to achieve a phase modulation amount of 2 pi. Then u is1＝1v,u2＝1.75v,u3＝2.5v,u4＝3.25v,u5At 4V (voltage range 1-4V), the minimum voltage is 1V. The corresponding relationship between the phase modulation amount and the voltage is
Of note areThe linear scaling coefficient L is not a fixed parameter when
The minimum voltage loaded is 1v, the difference is that
The values of the driving voltages are different, the values of other driving voltages are changed between 1V and 4V, and the proportionality coefficient is changed along with the change of the values of the driving voltages
Decreases and becomes smaller. When in use
At this time, the steering angle of the system is at a maximum, and 2 electrodes are needed to realize a phase modulation amount of 2 pi, so u1＝2.5v,u24v, then
The driving voltage u is not only related to the phase modulation amount, but also related to the tilt angle of the liquid crystal molecules, and the linear piecewise function is used for the average value of the voltage u and the tilt angle of the liquid crystal molecules
Fitting is carried out, and the fitting result is
Step four: due to maximum phase modulation
Therefore, the corresponding minimum voltage is 2.5v, and the linear function corresponding to the voltage of 0-3v in the formula (4) is substituted into the formula (3), so that the relation between the phase modulation amount and the average value of the tilt angle of the liquid crystal molecules can be obtained
By substituting the formula (9) into the formula (8), we can obtain the relationship between the beam deflection angle and the tilt angle of the liquid crystal molecules
Substituting the formulas (3) and (10) into the formula (2), we can obtain a fractional order model of the liquid crystal phased array beam deflection angle and the loaded phase delay amount.
Substituting the total delay tau of the system into the formula (11) can finally obtain a fractional order model of the beam deflection system of the liquid crystal phased array as
Step five: splay and bend viscosity coefficient η of liquid crystal in formula (5)1,η2Liquid crystal molecular body distribution charge coefficient j and fractional order alpha1And alpha2And the time lag coefficient tau is unknown, so the invention combines the Legendre wavelet integral operation technology to identify the model parameter.
Assuming a fractional order differential order α2Is the highest order in equation (13), and both ends of equation (13) are simultaneously divided by the fractional order α2We can get the fractional order integral equation:
expanding input and output of system by using Legendre wavelet
Wherein U isTAnd YTAs is known, the Legendre wavelet coefficients representing the input and output, respectively. The integral operation equation of Legendre wavelet is
The formula (16) may be rewritten in the form of a matrix. Order to
Equation (17) can be simplified to AX ═ B, and we solve the matrix X using least squares, first assuming a fractional order α2,α1If known, the matrix X can then be solved by
X＝(ATA)-1ATB (18)
Second, we set the fractional order α2,α1Substituting the model parameters X into equation (16), the system's identification output can be obtained
The output theta of the recognition systemp(t) and actual System output θaThe error of (t) can be defined as
Finally, we define the parameter identification intervals for the fractional orders and Z, and calculate their respective errors in the defined intervals by equation (19)And when the error is minimum, the corresponding fractional order and the model parameter are the identified optimal solution. The identification result is η2＝7.3076e-11,η1＝6.9062e-11,j＝695.0851,α2＝1.8,α10.9, and 3.027. FIG. 4 shows the fitting effect of the fractional order model and the integer order. It can be seen from the figure that when the loading phase difference is pi/2, the beam deflection angle gradually deflects from 0rad to 0.0272rad, the fractional order model established by the invention can well represent the beam deflection dynamic performance, and the fitting of the integer order model and actual data has a large error. This also verifies the validity of the fractional order model established by the present invention.
Claims (4)
1. A fractional order modeling method of a beam deflection system based on a liquid crystal phased array is characterized in that: the method comprises the following steps:
the method comprises the following steps: analyzing the stress deformation type of liquid crystal molecules in the liquid crystal phased array, and constructing a fractional order constitutive equation aiming at the deformation characteristic of the liquid crystal molecules under the action of an electric field
Wherein F (t) is the electric field force, η1,η2Viscosity coefficients of splay and bend, respectively, k1＝1.11×10-11N is the coefficient of elasticity, k, of splay2＝1.71×10-11N is the bending elastic coefficient, and theta (t) is the inclination angle of the liquid crystal director along the direction of the z axis;
step two: describing the distribution of liquid crystal molecular director under the action of electric field force by Gibbs free energy equation, and establishing fractional order constitutive equation of liquid crystal molecules in liquid crystal phased array by numerical averaging method
Where u (t) is the applied drive voltage, q is 1.6 × 10-19C is unit chargeJ is the distributed charge coefficient of the liquid crystal molecular body, and x is 9.8 mu m, which is the thickness of the liquid crystal layer;
step three: the corresponding relation between the phase difference and the driving voltage of the liquid crystal phased array, the driving voltage and the inclination angle of liquid crystal molecules is obtained by adopting a linear fitting method
Wherein, L is a proportionality coefficient,
is the average value of the tilt angles of the liquid crystal molecules;
step four: substituting the formula (3) and the formula (4) into the formula (2), and establishing a fractional order model of the liquid crystal phased array light beam deflection system by combining a liquid crystal phased array light beam regulation mechanism;
step five: and identifying unknown parameters and fractional orders of the fractional order model of the liquid crystal phased array beam deflection system by adopting a Legendre wavelet integral operation matrix method.
2. The fractional order modeling method for the liquid crystal phased array based beam deflection system according to claim 1, wherein in the first step, formula (1) is obtained by the following method:
the combination of an elastic element and a viscous element representing the viscoelasticity of the material, the elastic element obeying Hooke's law
σ(t)＝Hφ(t) (6)
Wherein, σ (t) is stress, φ (t) is strain, and H is elastic coefficient;
the viscous element is represented as
σ(t)＝KDαφ(t) (7)
Wherein K is the viscosity coefficient; dαIs of fractional orderA differential operator, α being a fractional order;
for a single liquid crystal molecule, the deformation process under the action of the electric field force F (t) can be described by the parallel connection of an elastic element and a viscous element, namely, the viscosity characteristic of the splay is divided by a fractional order viscous element
Denotes that the elasticity is given by k1θ (t) denotes, similarly, the viscosity of the bend is expressed as
Elasticity of bending is k2θ(t)，η1,η2Viscosity coefficients of splay and bend, respectively, k1＝1.11×10-11N is the coefficient of elasticity, k, of splay2＝1.71×10-11N is the bending elastic coefficient, theta (t) is the inclination angle of the liquid crystal director along the z-axis direction, and the constitutive equation of a single liquid crystal molecule is obtained
3. The fractional order modeling method for the liquid crystal phased array based beam deflection system according to claim 1 or 2, wherein in the second step, the formula (2) is obtained by the following method:
the voltage and the tilt angle of the director of the liquid crystal molecules can be approximated to be linear relation
The average value of the tilt angle of the liquid crystal molecules, the average value of the electric field force, assuming a uniform electric field, is the value of
Wherein q is 1.6 × 10-19C isThe electric quantity per unit charge, j is the liquid crystal molecular body distribution charge coefficient, x is 9.8 μm and is the liquid crystal layer thickness, equation (8) and
substituting into formula (1) to obtain fractional order constitutive equation of liquid crystal
4. The fractional order modeling method for the beam deflection system based on the liquid crystal phased array as claimed in claim 3, wherein the concrete method of the fourth step is: substituting the linear function corresponding to the voltage of 0-3v in the formula (4) obtained in the step three into the formula (3) to obtain the relation between the phase modulation amount and the average value of the tilt angles of the liquid crystal molecules
Substituting the formula (9) into the formula (8) yields the relationship between the beam deflection angle and the tilt angle of the liquid crystal molecules
Substituting the formulas (3) and (10) into the formula (2) to obtain a fractional order model of the liquid crystal phased array beam deflection angle and the loaded phase delay amount,
substituting the total time delay tau of the system into the formula (11), the fractional order model of the beam deflection system of the liquid crystal phased array can be obtained finally
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Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN115016165A (en) * | 2022-07-06 | 2022-09-06 | 西安工业大学 | Design method of coarse-fine two-stage synchronous regulation and control system of wide-angle liquid crystal optical phased array |
| CN117316337A (en) * | 2023-09-04 | 2023-12-29 | 中国人民解放军国防科技大学 | Numerical simulation method and device applied to defect structure in liquid crystal system |
| CN115016165B (en) * | 2022-07-06 | 2024-04-26 | 西安工业大学 | Design method of large-angle liquid crystal optical phased array coarse-fine two-stage synchronous regulation and control system |
Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US5151814A (en) * | 1987-08-19 | 1992-09-29 | Hughes Aircraft Company | Phased array for optical beam control |
| CN104865770A (en) * | 2015-05-11 | 2015-08-26 | 电子科技大学 | Method for achieving one-dimensional deflection and beam divergence angle scaling of laser beam based on optical phased array |
| CN109164662A (en) * | 2018-10-23 | 2019-01-08 | 长春理工大学 | Light beam based on liquid crystal optical phased array deflects control method |
| CN208903052U (en) * | 2018-10-23 | 2019-05-24 | 长春理工大学 | Laser radar light beam deflection closed loop control system based on liquid crystal optical phased array |
| CN110398850A (en) * | 2019-07-04 | 2019-11-01 | 西安工业大学 | Multichannel liquid crystal programmable phase modulating system based on MCU |
-
2022
- 2022-03-23 CN CN202210287990.6A patent/CN114675443A/en active Pending
Patent Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US5151814A (en) * | 1987-08-19 | 1992-09-29 | Hughes Aircraft Company | Phased array for optical beam control |
| CN104865770A (en) * | 2015-05-11 | 2015-08-26 | 电子科技大学 | Method for achieving one-dimensional deflection and beam divergence angle scaling of laser beam based on optical phased array |
| CN109164662A (en) * | 2018-10-23 | 2019-01-08 | 长春理工大学 | Light beam based on liquid crystal optical phased array deflects control method |
| CN208903052U (en) * | 2018-10-23 | 2019-05-24 | 长春理工大学 | Laser radar light beam deflection closed loop control system based on liquid crystal optical phased array |
| CN110398850A (en) * | 2019-07-04 | 2019-11-01 | 西安工业大学 | Multichannel liquid crystal programmable phase modulating system based on MCU |
Non-Patent Citations (3)
| Title |
|---|
| 杜升平等: "基于相控阵雷达模型的液晶光束偏转波控方法研究", 应用光学, no. 04, 15 July 2017 (2017-07-15) * |
| 王春阳等: "基于液晶相控阵的光束偏转控制方法研究", 液晶与显示, no. 10, 15 October 2018 (2018-10-15) * |
| 郑青泉等: "斜入射下液晶偏振光栅衍射特性研究", 红外与激光工程, vol. 51, no. 7, 8 November 2021 (2021-11-08) * |
Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN115016165A (en) * | 2022-07-06 | 2022-09-06 | 西安工业大学 | Design method of coarse-fine two-stage synchronous regulation and control system of wide-angle liquid crystal optical phased array |
| CN115016165B (en) * | 2022-07-06 | 2024-04-26 | 西安工业大学 | Design method of large-angle liquid crystal optical phased array coarse-fine two-stage synchronous regulation and control system |
| CN117316337A (en) * | 2023-09-04 | 2023-12-29 | 中国人民解放军国防科技大学 | Numerical simulation method and device applied to defect structure in liquid crystal system |
| CN117316337B (en) * | 2023-09-04 | 2024-03-29 | 中国人民解放军国防科技大学 | Numerical simulation method and device applied to defect structure in liquid crystal system |
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