[go: up one dir, main page]

CN119001681A - Design method for dihedral angle errors of single corner reflector - Google Patents

Design method for dihedral angle errors of single corner reflector Download PDF

Info

Publication number
CN119001681A
CN119001681A CN202410936898.7A CN202410936898A CN119001681A CN 119001681 A CN119001681 A CN 119001681A CN 202410936898 A CN202410936898 A CN 202410936898A CN 119001681 A CN119001681 A CN 119001681A
Authority
CN
China
Prior art keywords
corner reflector
wave
matrix
far
vector
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Pending
Application number
CN202410936898.7A
Other languages
Chinese (zh)
Inventor
韩西达
何智昭
李明
李江湖
李昱祚
吴先霖
林旭东
赵宏超
刘祺
叶贤基
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Sun Yat Sen University
Original Assignee
Sun Yat Sen University
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Sun Yat Sen University filed Critical Sun Yat Sen University
Priority to CN202410936898.7A priority Critical patent/CN119001681A/en
Publication of CN119001681A publication Critical patent/CN119001681A/en
Pending legal-status Critical Current

Links

Classifications

    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/48—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S17/00
    • G01S7/497—Means for monitoring or calibrating
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S17/00—Systems using the reflection or reradiation of electromagnetic waves other than radio waves, e.g. lidar systems
    • G01S17/02—Systems using the reflection of electromagnetic waves other than radio waves
    • G01S17/06—Systems determining position data of a target
    • G01S17/08—Systems determining position data of a target for measuring distance only
    • G01S17/10—Systems determining position data of a target for measuring distance only using transmission of interrupted, pulse-modulated waves
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/48—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S17/00
    • G01S7/483—Details of pulse systems
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/14—Force analysis or force optimisation, e.g. static or dynamic forces

Landscapes

  • Engineering & Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Computer Networks & Wireless Communication (AREA)
  • Radar, Positioning & Navigation (AREA)
  • Remote Sensing (AREA)
  • Theoretical Computer Science (AREA)
  • Electromagnetism (AREA)
  • Geometry (AREA)
  • General Engineering & Computer Science (AREA)
  • Evolutionary Computation (AREA)
  • Computer Hardware Design (AREA)
  • Optical Communication System (AREA)

Abstract

The invention discloses a design method of dihedral angle errors of a single corner reflector, which comprises the following steps: calculating according to the number of the tracks of the ranging target to obtain the variation range of the speed difference angle; constructing a far-field diffraction model based on the dihedral angle error compensation speed difference effect; inputting parameters of a corner reflector and ranging laser and the variation range of the speed difference angle as input conditions to the far-field diffraction model, and performing far-field diffraction simulation on the corner reflector with dihedral angle errors through a Fraunhofer formula in the far-field diffraction model to obtain corresponding far-field energy distribution; and calculating according to the far-field energy distribution to obtain the dihedral angle error of the optimal corner reflector. The dihedral angle error design method provided by the invention has strong universality and can be applied to various laser ranging scenes.

Description

Design method for dihedral angle errors of single corner reflector
Technical Field
The invention relates to the field of laser ranging, in particular to a design method of dihedral angle errors of a single corner reflector.
Background
The corner reflector is a tetrahedral prism in which three surfaces are perpendicular to each other, called a reflecting surface, and a fourth surface may be divided into a rounded bottom surface and a triangular bottom surface according to whether or not it is cut. When the laser enters the corner reflector through the bottom surface, the laser exits through the bottom surface after three total reflections of the three reflecting surfaces. The direction of the outgoing laser light is exactly opposite to the direction of the incoming laser light. This retro-reflection characteristic is independent of the direction of incidence of the laser light.
When laser light is obliquely incident on the corner reflector array, since it is not known through which corner reflector the echo pulse is reflected back, the laser pulse is widened to introduce a ranging error. Therefore, the monolithic corner reflector has been the major considered corner reflector object at present.
The 100mm bore solid corner reflectors currently developed by university of maryland in the united states have been completed and optical testing has been completed. The current corner reflector design is mainly aimed at lunar laser ranging, the considered corner reflector is a solid corner reflector, default laser has polarization characteristics, and the design method lacks universality.
Disclosure of Invention
In order to solve the technical problems of single target and poor universality in the design of the corner reflectors in the prior art, the invention provides a design method for dihedral angle errors of a single corner reflector, which comprises the following steps:
Calculating according to the number of the tracks of the ranging target to obtain the variation range of the speed difference angle;
constructing a far-field diffraction model based on the dihedral angle error compensation speed difference effect;
Inputting parameters of a corner reflector and ranging laser and the variation range of the speed difference angle as input conditions to the far-field diffraction model, and performing far-field diffraction simulation on the corner reflector with dihedral angle errors through a Fraunhofer formula in the far-field diffraction model to obtain corresponding far-field energy distribution;
and calculating according to the far-field energy distribution to obtain the dihedral angle error of the optimal corner reflector.
As a preferred embodiment, the method for calculating the range of the slip angle according to the number of the tracks of the ranging target includes:
and calculating according to the track number of the ranging target to obtain a linear velocity vector of the ranging target, performing difference between the linear velocity vector and the linear velocity vector of the station rotation, and projecting the linear velocity vector to a direction perpendicular to the ranging target-station vector for calculation to obtain the variation range of the speed difference angle of the ranging target.
As a preferred embodiment, the magnitude of the slip angle is calculated by the following formula:
Wherein v r is the projection of the motion speed of the satellite relative to the station in the direction perpendicular to the ranging target-station vector, and c is the speed of light; the motion speed of the satellite satisfies the vitality formula:
Wherein v is the linear velocity of the satellite revolving around the earth, G is the gravitational constant of the earth, r is the distance from the satellite to the earth centroid, and a is the semi-long axis of the satellite orbit; the station also has a rotational linear velocity on earth that satisfies:
where ω is the angular velocity of earth rotation, RE is the earth radius, Is the latitude where the station is located.
As a preferred scheme, the method for constructing the far-field diffraction model comprises the following steps:
Far field diffraction is calculated by using the Fraunhofer formula, and the specific formula is as follows:
Wherein z 1 represents the distance from the diffraction plane to the viewing plane, x 1,y1 is the abscissa and ordinate of the diffraction plane, respectively, x, y is the abscissa and ordinate of the viewing plane, respectively, wherein the second term is a secondary phase factor, which has no influence on the intensity of light, Is a spherical wave with an amplitude of 1,For the complex amplitude over the diffraction aperture,Is the wave number, thus setThe fraunhofer formula is simplified to:
as a secondary phase factor, the energy distribution of the far-field diffraction light spot is calculated without influence, so that the energy distribution is ignored; the final fraunhofer formula is as follows:
as a preferred scheme, the method for constructing the far-field diffraction model further comprises the following steps: calculating a far-field diffraction image of the corner reflector through wavefront distribution of the diffraction plane; the wavefront distribution of the diffraction plane is quantitatively described by establishing two coordinate systems, specifically:
Establishing a pyramid coordinate system o-xyz through three right-angle sides of the corner reflector, wherein o is the vertex of the corner reflector; establishing a bottom surface coordinate system o ' -x ' y ' z ' on the bottom surface of the corner reflector, wherein o ' is the projection of a vertex on the bottom surface, is also the center of the bottom surface of the corner reflector, the z ' axis is the normal direction of the bottom surface, the y ' axis direction is the projection of the y axis on the bottom surface, and o ' -x ' y ' z ' forms a right-hand system; since the incident light vector and the reflected light vector are symmetrical with respect to the reflecting surface, calculation can be performed by a mirror image conversion method; the Household matrix of the mirror transformation is related to the normal vector of the reflecting surface; in the pyramid coordinate system, normal vectors of the three reflecting surfaces are respectively an x axis, a y axis and a z axis.
As a preferred embodiment, the transformation matrix of the bottom surface coordinate system and the pyramid coordinate system is as follows:
Wherein the method comprises the steps of As a vector in the pyramid coordinate system,Is a vector in the bottom surface coordinate system.
As a preferred scheme, the method for constructing the far-field diffraction model further comprises the following steps:
The far-field diffraction simulation taking the polarization characteristics of laser into consideration is specifically as follows:
For the calculation of polarized light, a jones vector is used to describe linearly polarized light or circularly polarized light; for linearly polarized light, expressed as: θ is the polarization angle of the linearly polarized light, the magnitude of which is the angle between the polarization direction of the linearly polarized light and the x-axis of the coordinate system, expressed as circularly polarized light The + -respectively corresponds to the left-hand and right-hand of the circularly polarized light; the total reflection process changes the phases of s-waves and p-waves only, and therefore this process is represented by a jones matrix: Delta s,δp represents the phase change of s wave and p wave in the process of total reflection;
Expanding the jones vector and the jones matrix to three dimensions;
Decomposing laser to directions perpendicular to an incident surface and parallel to the incident surface, namely s-wave and p-wave, transmitting the laser in the corner reflector, and establishing a coordinate system to quantitatively describe the changes of the directions and phases of the s-wave and the p-wave in the transmission process of the laser in the corner reflector;
For polarized light, p, s, k constitute the right-hand system, and can be derived from the physical meaning of s-waves:
Wherein N represents a normal to an incident surface of the corner reflector;
defining a light vector in a pyramid coordinate system in a light ray tracing process;
Before the Jones matrix is applied to carry out phase superposition on the s wave and the p wave, a matrix is introduced to realize the conversion of a coordinate system; the fresnel formula for each refraction or reflection process is represented by a matrix and the change in the q-th surface light vector is represented by matrix P q:
Because p, s and k form a right-hand system, the matrices are all orthogonal matrices, namely the inverse matrix is equal to the transposed matrix; j q is a three-dimensional jones matrix representing the q-th surface; a s,q and a p,q are respectively the transmission or reflection coefficients of s wave and p wave, and are calculated by a Fresnel formula, and are determined according to the occurring optical process; The matrix is used for converting the light vector in the pyramid coordinate system into the (s q,pq,kq-1) coordinate system; the O out,q matrix functions to convert the light vector in the (s q,pq′,kq) coordinate system into the pyramid coordinate system; s q represents the s-wave component of the refraction or reflection process of the q-th surface; p q represents the p-wave component before refraction or reflection occurs on the q-th surface, obtained by cross-multiplying s q with k q-0; k q-1 represents the emergent light vector of the (q-1) th surface under the pyramid coordinate system, and k q is the same; p q' represents the p-wave component of the outgoing light after the refractive or reflective process has occurred on the q-th surface;
the polarization state change of the laser light after passing through the corner reflector is described by 5 matrix multiplication; the 5 matrices respectively correspond to 5 refraction or reflection processes, and the 5 matrices are respectively marked as a first matrix, a second matrix, a third matrix, a fourth matrix and a fifth matrix, specifically:
The corresponding process of the first matrix is as follows: laser is incident to the bottom surface of the corner reflector to be refracted;
The corresponding processes of the second matrix, the third matrix and the fourth matrix are as follows: the laser light is totally reflected at the three reflecting surfaces;
The fifth matrix corresponds to the process: the laser is refracted through the bottom surface and then is emitted from the inside of the corner reflector to the outside space; the entire calculation process is an iterative process, and the initial definition of s 0,p0 and p 0' is:
p0＝s0×k0
p'0＝s'0×k'0
k '0 represents the light vector of k 0 after refraction or reflection, P matrices of 5 processes are calculated based on s 0,p0 and P 0', and finally the final exit vector is obtained by multiplying the 5P matrices and then multiplying the incident polarization vector by the left.
As a preferable scheme, the direction and phase change of s wave and p wave in the internal transmission process of the corner reflector are specifically as follows:
In the process of transmitting laser in the corner reflector, the laser can undergo twice refraction and three times of total reflection; the refraction only changes the amplitude of the s wave and the p wave, and does not change the phase of the s wave and the p wave; in the process of three times of total reflection, the amplitudes of the s wave and the p wave are unchanged, and the phase is changed; in each total reflection process, the incident surfaces of the lasers are different, so that the phases and directions of the s wave and the p wave are changed.
As a preferred aspect, the corner reflector includes a solid corner reflector and a hollow corner reflector.
As a preferred embodiment, the method for calculating the optimum corner reflector dihedral angle error from the far-field energy distribution in the variation range of the slip angle includes:
And taking the normalized energy mean value of far-field energy distribution in the variation range of the speed difference angle as an evaluation index to obtain the optimal dihedral angle error design of the corner reflector.
Compared with the prior art, the invention has the following beneficial effects:
The method can obtain the corresponding track number according to different ranging targets, and then design the optimal dihedral angle errors of different aperture corner reflectors by using a far-field diffraction model;
The invention can calculate the relative echo photon number under the condition of considering the factors of the caliber of the corner reflector, dihedral angle error, speed difference angle range, laser incidence angle and the like.
Drawings
Fig. 1 is a flow chart of a design method of dihedral angle errors of a monolithic corner reflector according to the present embodiment;
Fig. 2 is a schematic diagram of a coordinate system provided in the present embodiment.
Detailed Description
The drawings are for illustrative purposes only and are not to be construed as limiting the invention;
it should be understood that the described embodiments are merely some, but not all embodiments of the present application. All other embodiments, which can be made by one of ordinary skill in the art without undue burden from the application, are intended to be within the scope of the embodiments of the present application.
The terminology used in the embodiments of the application is for the purpose of describing particular embodiments only and is not intended to be limiting of embodiments of the application. As used in this application and the appended claims, the singular forms "a," "an," and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise. It should also be understood that the term "and/or" as used herein refers to and encompasses any or all possible combinations of one or more of the associated listed items.
When the following description refers to the accompanying drawings, the same numbers in different drawings refer to the same or similar elements, unless otherwise indicated. The implementations described in the following exemplary examples do not represent all implementations consistent with the application. Rather, they are merely examples of apparatus and methods consistent with certain aspects of the application as detailed in the accompanying claims. In the description of the present application, it should be understood that the terms "first," "second," "third," and the like are used merely to distinguish between similar objects and are not necessarily used to describe a particular order or sequence, nor should they be construed to indicate or imply relative importance. The specific meaning of the above terms in the present application can be understood by those of ordinary skill in the art according to the specific circumstances.
Furthermore, in the description of the present application, unless otherwise indicated, "a plurality" means two or more. "and/or", describes an association relationship of an association object, and indicates that there may be three relationships, for example, a and/or B, and may indicate: a exists alone, A and B exist together, and B exists alone. The character "/" generally indicates that the context-dependent object is an "or" relationship. The application is further illustrated in the following figures and examples.
The invention is further illustrated in the following figures and examples.
Example 1
Referring to fig. 1, the present embodiment provides a method for designing dihedral angle errors of a monolithic corner reflector, the method comprising:
s1: calculating according to the number of the tracks of the ranging target to obtain the variation range of the speed difference angle;
s2: constructing a far-field diffraction model based on the dihedral angle error compensation speed difference effect;
S3: inputting parameters of a corner reflector and ranging laser and the variation range of the speed difference angle as input conditions to the far-field diffraction model, and performing far-field diffraction simulation on the corner reflector with dihedral angle errors through a Fraunhofer formula in the far-field diffraction model to obtain corresponding far-field energy distribution;
Specifically, the input conditions of the far-field diffraction model further comprise the bottom surface caliber of the corner reflector and the ranging laser wavelength.
S4: and calculating according to the far-field energy distribution to obtain the dihedral angle error of the optimal corner reflector.
In a specific embodiment, the method for calculating the range of the slip angle according to the track number of the ranging target comprises the following steps:
and calculating according to the track number of the ranging target to obtain a linear velocity vector of the ranging target, performing difference between the linear velocity vector and the linear velocity vector of the station rotation, and projecting the linear velocity vector to a direction perpendicular to the ranging target-station vector for calculation to obtain the variation range of the speed difference angle of the ranging target.
In a specific embodiment, the magnitude of the slip angle is calculated by the following formula:
Wherein v r is the projection of the motion speed of the satellite relative to the station in the direction perpendicular to the ranging target-station vector, and c is the speed of light; the motion speed of the satellite satisfies the vitality formula:
Wherein v is the linear velocity of the satellite revolving around the earth, G is the gravitational constant of the earth, r is the distance from the satellite to the earth centroid, and a is the semi-long axis of the satellite orbit; the station also has a rotational linear velocity on earth that satisfies:
where ω is the angular velocity of earth rotation, RE is the earth radius, Is the latitude where the station is located.
In a specific embodiment, the method of constructing a far field diffraction model includes:
Far field diffraction is calculated by using the Fraunhofer formula, and the specific formula is as follows:
Wherein z 1 represents the distance from the diffraction plane to the viewing plane, x 1,y1 is the abscissa and ordinate of the diffraction plane, respectively, x, y is the abscissa and ordinate of the viewing plane, respectively, wherein the second term is a secondary phase factor, which has no influence on the intensity of light, Is a spherical wave with an amplitude of 1,For the complex amplitude over the diffraction aperture,Is the wave number, thus setThe fraunhofer formula is simplified to:
as a secondary phase factor, the energy distribution of the far-field diffraction light spot is calculated without influence, so that the energy distribution is ignored; the final fraunhofer formula is as follows:
In a specific embodiment, the method of constructing a far field diffraction model further comprises: calculating a far-field diffraction image of the corner reflector through wavefront distribution of the diffraction plane; the wavefront distribution of the diffraction plane is quantitatively described by establishing two coordinate systems, specifically:
Referring to fig. 2, a pyramid coordinate system o-xyz is established through three right-angle sides of the corner reflector, where o is the vertex of the corner reflector; establishing a bottom surface coordinate system o ' -x ' y ' z ' on the bottom surface of the corner reflector, wherein o ' is the projection of a vertex on the bottom surface, is also the center of the bottom surface of the corner reflector, the z ' axis is the normal direction of the bottom surface, the y ' axis direction is the projection of the y axis on the bottom surface, and o ' -x ' y ' z ' forms a right-hand system; since the incident light vector and the reflected light vector are symmetrical with respect to the reflecting surface, calculation can be performed by a mirror image conversion method; the Household matrix of the mirror transformation is related to the normal vector of the reflecting surface; in the pyramid coordinate system, normal vectors of the three reflecting surfaces are respectively an x axis, a y axis and a z axis.
In a specific embodiment, the transformation matrix of the bottom surface coordinate system and the pyramid coordinate system is as follows:
Wherein the method comprises the steps of As a vector in the pyramid coordinate system,Is a vector in the bottom surface coordinate system.
In a specific embodiment, the corner reflectors include solid corner reflectors and hollow corner reflectors.
In a specific embodiment, the method for calculating the optimal corner reflector dihedral angle error according to the far field energy distribution in the variation range of the slip angle comprises the following steps:
And taking the normalized energy mean value of far-field energy distribution in the variation range of the speed difference angle as an evaluation index to obtain the optimal dihedral angle error design of the corner reflector.
Example 2
Referring to fig. 1, this embodiment can be regarded as a modified or extended embodiment of embodiment 1, specifically:
a method of designing dihedral angle errors for a monolithic corner reflector, the method comprising:
s1: calculating according to the number of the tracks of the ranging target to obtain the variation range of the speed difference angle;
s2: constructing a far-field diffraction model based on the dihedral angle error compensation speed difference effect;
S3: inputting parameters of a corner reflector and ranging laser and the variation range of the speed difference angle as input conditions to the far-field diffraction model, and performing far-field diffraction simulation on the corner reflector with dihedral angle errors through a Fraunhofer formula in the far-field diffraction model to obtain corresponding far-field energy distribution;
Specifically, the input conditions of the far-field diffraction model further comprise the bottom surface caliber of the corner reflector and the ranging laser wavelength.
S4: and calculating according to the far-field energy distribution to obtain the dihedral angle error of the optimal corner reflector.
In a specific embodiment, the method for calculating the range of the slip angle according to the track number of the ranging target comprises the following steps:
and calculating according to the track number of the ranging target to obtain a linear velocity vector of the ranging target, performing difference between the linear velocity vector and the linear velocity vector of the station rotation, and projecting the linear velocity vector to a direction perpendicular to the ranging target-station vector for calculation to obtain the variation range of the speed difference angle of the ranging target.
In a specific embodiment, the magnitude of the slip angle is calculated by the following formula:
Wherein v r is the projection of the motion speed of the satellite relative to the station in the direction perpendicular to the ranging target-station vector, and c is the speed of light; the motion speed of the satellite satisfies the vitality formula:
Wherein v is the linear velocity of the satellite revolving around the earth, G is the gravitational constant of the earth, r is the distance from the satellite to the earth centroid, and a is the semi-long axis of the satellite orbit; the station also has a rotational linear velocity on earth that satisfies:
where ω is the angular velocity of earth rotation, RE is the earth radius, Is the latitude where the station is located.
In a specific embodiment, the method of constructing a far field diffraction model includes:
Far field diffraction is calculated by using the Fraunhofer formula, and the specific formula is as follows:
Wherein z 1 represents the distance from the diffraction plane to the viewing plane, x 1,y1 is the abscissa and ordinate of the diffraction plane, respectively, x, y is the abscissa and ordinate of the viewing plane, respectively, wherein the second term is a secondary phase factor, which has no influence on the intensity of light, Is a spherical wave with an amplitude of 1,For the complex amplitude over the diffraction aperture,Is the wave number, thus setThe fraunhofer formula is simplified to:
as a secondary phase factor, the energy distribution of the far-field diffraction light spot is calculated without influence, so that the energy distribution is ignored; the final fraunhofer formula is as follows:
note that if only the relative distribution of energy is considered, the constant term outside the integral can be ignored, and then the above equation is the same as the form of the two-dimensional fourier transform, so that calculation of fraunhofer diffraction can be regarded as fourier transform of complex amplitude over the diffraction aperture.
In a specific embodiment, the method of constructing a far field diffraction model further comprises: calculating a far-field diffraction image of the corner reflector through wavefront distribution of the diffraction plane; the wavefront distribution of the diffraction plane is quantitatively described by establishing two coordinate systems, specifically:
Referring to fig. 2, a pyramid coordinate system o-xyz is established through three right-angle sides of the corner reflector, where o is the vertex of the corner reflector; establishing a bottom surface coordinate system o ' -x ' y ' z ' on the bottom surface of the corner reflector, wherein o ' is the projection of a vertex on the bottom surface, is also the center of the bottom surface of the corner reflector, the z ' axis is the normal direction of the bottom surface, the y ' axis direction is the projection of the y axis on the bottom surface, and o ' -x ' y ' z ' forms a right-hand system; since the incident light vector and the reflected light vector are symmetrical with respect to the reflecting surface, calculation can be performed by a mirror image conversion method; the Household matrix of the mirror transformation is related to the normal vector of the reflecting surface; in the pyramid coordinate system, normal vectors of the three reflecting surfaces are respectively an x axis, a y axis and a z axis.
In a specific embodiment, the transformation matrix of the bottom surface coordinate system and the pyramid coordinate system is as follows:
Wherein the method comprises the steps of As a vector in the pyramid coordinate system,Is a vector in the bottom surface coordinate system;
It should be noted that the specific principle is to artificially control the three reflecting surfaces of the corner reflector so that the three reflecting surfaces are not strictly vertical any more. When a plane wave is incident on such a corner reflector, the reflected light spot will split to some extent, thereby greatly increasing the number of echo photons at the slip angle. The compensation effect of the method on the large-caliber corner reflector is particularly obvious.
In a specific embodiment, the method of constructing a far field diffraction model further comprises:
The far-field diffraction simulation taking the polarization characteristics of laser into consideration is specifically as follows:
For the calculation of polarized light, a jones vector is used to describe linearly polarized light or circularly polarized light; for linearly polarized light, expressed as: θ is the polarization angle of the linearly polarized light, the magnitude of which is the angle between the polarization direction of the linearly polarized light and the x-axis of the coordinate system, expressed as circularly polarized light The + -respectively corresponds to the left-hand and right-hand of the circularly polarized light; the total reflection process changes the phases of s-waves and p-waves only, and therefore this process is represented by a jones matrix: Delta s,δp represents the phase change of s wave and p wave in the process of total reflection;
Expanding the jones vector and the jones matrix to three dimensions;
Decomposing laser to directions perpendicular to an incident surface and parallel to the incident surface, namely s-wave and p-wave, transmitting the laser in the corner reflector, and establishing a coordinate system to quantitatively describe the changes of the directions and phases of the s-wave and the p-wave in the transmission process of the laser in the corner reflector;
For polarized light, p, s, k constitute the right-hand system, and can be derived from the physical meaning of s-waves:
Wherein N represents a normal to an incident surface of the corner reflector;
Specifically, the incident light vector k q for the q-th surface is actually the refractive/reflective light vector k q-1 for the q-1 th surface. Thus, the ray tracing problem of polarized light is essentially an iterative process, and the output of the last refraction/reflection process is the input of the next refraction/reflection process.
In order to facilitate calculation of the reflected light vector, defining the light vector in a pyramid coordinate system in the process of ray tracing;
since the direction and phase of s-wave and p-wave will change with each reflection. Therefore, the phase change amounts of the three total reflections cannot be simply superimposed as the total amount of phase change;
Before the Jones matrix is applied to carry out phase superposition on the s wave and the p wave, a matrix is introduced to realize the conversion of a coordinate system; the fresnel formula for each refraction or reflection process is represented by a matrix and the change in the q-th surface light vector is represented by matrix P q:
Because p, s and k form a right-hand system, the matrices are all orthogonal matrices, namely the inverse matrix is equal to the transposed matrix; j q is a three-dimensional jones matrix representing the q-th surface; a s,q and a p,q are respectively the transmission or reflection coefficients of s wave and p wave, and are calculated by a Fresnel formula, and are determined according to the occurring optical process; The matrix is used for converting the light vector in the pyramid coordinate system into the (s q,pq,kq-1) coordinate system; the O out,q matrix functions to convert the light vector in the (s q,pq′,kq) coordinate system into the pyramid coordinate system; s q represents the s-wave component of the refraction or reflection process of the q-th surface; p q represents the p-wave component before refraction or reflection occurs on the q-th surface, obtained by cross-multiplying s q with k q-1; k q-1 represents the emergent light vector of the (q-1) th surface under the pyramid coordinate system, and k q is the same; p q' represents the p-wave component of the outgoing light after the refractive or reflective process has occurred on the q-th surface;
the polarization state change of the laser light after passing through the corner reflector is described by 5 matrix multiplication; the 5 matrices respectively correspond to 5 refraction or reflection processes, and the 5 matrices are respectively marked as a first matrix, a second matrix, a third matrix, a fourth matrix and a fifth matrix, specifically:
The corresponding process of the first matrix is as follows: laser is incident to the bottom surface of the corner reflector to be refracted;
The corresponding processes of the second matrix, the third matrix and the fourth matrix are as follows: the laser light is totally reflected at the three reflecting surfaces;
The fifth matrix corresponds to the process: the laser is refracted through the bottom surface and then is emitted from the inside of the corner reflector to the outside space; the entire calculation process is an iterative process, and the initial definition of s 0,p0 and p 0' is:
p0＝s0×k0
p'0＝s'0×k'0
k '0 represents the light vector of k 0 after refraction or reflection, P matrices of 5 processes are calculated based on s 0,p0 and P 0', and finally the final exit vector is obtained by multiplying the 5P matrices and then multiplying the incident polarization vector by the left.
In a specific embodiment, the direction and phase change of the s wave and the p wave in the process of transmitting the laser inside the corner reflector are specifically as follows:
In the process of transmitting laser in the corner reflector, the laser can undergo twice refraction and three times of total reflection; the refraction only changes the amplitude of the s wave and the p wave, and does not change the phase of the s wave and the p wave; in the process of three times of total reflection, the amplitudes of the s wave and the p wave are unchanged, and the phase is changed; in each total reflection process, the incident surfaces of the lasers are different, so that the phases and directions of the s wave and the p wave are changed.
In a specific embodiment, the corner reflectors include solid corner reflectors and hollow corner reflectors.
In a specific embodiment, the method for calculating the optimal corner reflector dihedral angle error according to the far field energy distribution in the variation range of the slip angle comprises the following steps:
And taking the normalized energy mean value of far-field energy distribution in the variation range of the speed difference angle as an evaluation index to obtain the optimal dihedral angle error design of the corner reflector.
It is to be understood that the above examples of the present invention are provided by way of illustration only and not by way of limitation of the embodiments of the present invention. Other variations or modifications of the above teachings will be apparent to those of ordinary skill in the art. It is not necessary here nor is it exhaustive of all embodiments. Any modification, equivalent replacement, improvement, etc. which come within the spirit and principles of the invention are desired to be protected by the following claims.

Claims (10)

1.一种单体角反射器二面角误差的设计方法，其特征在于，所述方法包括：1. A method for designing dihedral angle error of a single corner reflector, characterized in that the method comprises: 根据测距目标的轨道根数计算得到速差角的变化范围；The variation range of the velocity difference angle is calculated according to the orbital elements of the ranging target; 基于二面角误差补偿速差效应，构建远场衍射模型；Based on the dihedral error compensation speed difference effect, a far-field diffraction model is constructed; 将角反射器、测距激光的参数以及所述速差角的变化范围作为输入条件输入到所述远场衍射模型，通过所述远场衍射模型中的夫琅禾费公式对存在二面角误差的角反射器进行远场衍射仿真，得到对应的远场能量分布；Inputting the parameters of the corner reflector, the ranging laser and the variation range of the speed difference angle as input conditions into the far-field diffraction model, performing far-field diffraction simulation on the corner reflector with dihedral angle error through the Fraunhofer formula in the far-field diffraction model, and obtaining the corresponding far-field energy distribution; 根据所述远场能量分布计算得到最优角反射器二面角误差。The optimal corner reflector dihedral error is calculated based on the far-field energy distribution. 2.根据权利要求1所述的一种单体角反射器二面角误差的设计方法，其特征在于，根据测距目标的轨道根数计算得到速差角范围的方法包括：2. The design method of the dihedral angle error of a single corner reflector according to claim 1, characterized in that the method of calculating the speed difference angle range according to the track elements of the ranging target comprises: 根据测距目标的轨道根数计算得到测距目标的线速度矢量，在与台站自转的线速度矢量作差后再投影到垂直于测距目标-台站矢量方向上进行计算得到测距目标的速差角的变化范围。The linear velocity vector of the ranging target is calculated according to the orbital roots of the ranging target. After subtracting it from the linear velocity vector of the station's rotation, it is projected to the direction perpendicular to the ranging target-station vector to calculate the range of the velocity difference angle of the ranging target. 3.根据权利要求2所述的一种单体角反射器二面角误差的设计方法，其特征在于，速差角的大小通过以下公式计算：3. The design method of the dihedral angle error of a single corner reflector according to claim 2, characterized in that the magnitude of the speed difference angle is calculated by the following formula: 其中vr为卫星相对于台站的运动速度在垂直于测距目标-台站矢量方向上的投影，c为光速；卫星的运动速度满足活力公式：Where v r is the projection of the satellite's velocity relative to the station in the direction perpendicular to the ranging target-station vector, and c is the speed of light; the satellite's velocity satisfies the vitality formula: 其中v为卫星绕地球公转的线速度，G为地球引力常数，r为卫星到地球质心的距离，a为卫星轨道的半长轴；同样台站在地球上也有一个自转的线速度满足：Where v is the linear velocity of the satellite orbiting the earth, G is the earth's gravitational constant, r is the distance from the satellite to the earth's center of mass, and a is the semi-major axis of the satellite's orbit; similarly, the station also has a linear velocity of rotation on the earth that satisfies: 其中ω为地球自转的角速度，RE为地球半径，为台站所处的纬度。Where ω is the angular velocity of the Earth's rotation, RE is the radius of the Earth, is the latitude of the station. 4.根据权利要求3所述的一种单体角反射器二面角误差的设计方法，其特征在于，构建远场衍射模型的方法包括：4. The method for designing the dihedral angle error of a single corner reflector according to claim 3, wherein the method for constructing a far-field diffraction model comprises: 通过夫琅禾费公式计算远场衍射，具体公式为：The far-field diffraction is calculated by the Fraunhofer formula. The specific formula is: 其中，z1表示从衍射平面到观察平面的距离，x1,y1分别为衍射平面的横坐标和纵坐标，x,y分别为观察平面的横坐标和纵坐标，式中第二项为一个二次相位因子，对光的强度没有影响，是一个振幅为1的球面波，为衍射孔径上的复振幅，为波数，因此设所述夫琅禾费公式简化为：Among them, z 1 represents the distance from the diffraction plane to the observation plane, x 1 and y 1 are the horizontal and vertical coordinates of the diffraction plane, and x and y are the horizontal and vertical coordinates of the observation plane, respectively. The second term in the formula is a quadratic phase factor, which has no effect on the intensity of light. is a spherical wave with an amplitude of 1. is the complex amplitude at the diffraction aperture, is the wave number, so let The Fraunhofer formula simplifies to: 为一个二次相位因子，对计算远场衍射光斑能量分布没有影响，因此将其忽略；最终得到夫琅禾费公式如下： is a quadratic phase factor, which has no effect on the calculation of the energy distribution of the far-field diffraction spot, so it is ignored; the final Fraunhofer formula is as follows: 5.根据权利要求4所述的一种单体角反射器二面角误差的设计方法，其特征在于，构建远场衍射模型的方法还包括：通过衍射平面的波前分布计算角反射器的远场衍射图像；所述衍射平面的波前分布通过建立两个坐标系进行定量描述，具体为：5. According to the design method of the dihedral angle error of a single corner reflector according to claim 4, it is characterized in that the method of constructing the far-field diffraction model further comprises: calculating the far-field diffraction image of the corner reflector through the wavefront distribution of the diffraction plane; the wavefront distribution of the diffraction plane is quantitatively described by establishing two coordinate systems, specifically: 通过角反射器的三条直角边建立角锥坐标系o-xyz，o为角反射器的顶点；在角反射器的底面上建立底面坐标系o′-x′y′z′，o′为顶点在底面的投影，亦为角反射器底面中心，z′轴为底面的法线方向，y′轴方向为y轴在底面上的投影，o′-x′y′z′构成右手系；由于入射光矢量与反射光矢量关于反射面对称，因此，能够通过镜像变换的方法进行计算；镜像变换的Household矩阵与反射面的法线矢量有关；在角锥坐标系内，三个反射面的法线矢量分别为x轴，y轴与z轴。A corner cone coordinate system o-xyz is established through the three right-angled sides of the corner reflector, where o is the vertex of the corner reflector; a bottom surface coordinate system o′-x′y′z′ is established on the bottom surface of the corner reflector, where o′ is the projection of the vertex on the bottom surface, which is also the center of the bottom surface of the corner reflector, the z′ axis is the normal direction of the bottom surface, the y′ axis direction is the projection of the y axis on the bottom surface, and o′-x′y′z′ constitutes a right-handed system; since the incident light vector and the reflected light vector are symmetric about the reflection surface, they can be calculated by the mirror transformation method; the Household matrix of the mirror transformation is related to the normal vector of the reflection surface; in the corner cone coordinate system, the normal vectors of the three reflection surfaces are the x-axis, y-axis and z-axis respectively. 6.根据权利要求5所述的一种单体角反射器二面角误差的设计方法，其特征在于，所述底面坐标系与所述角锥坐标系的转换矩阵如下：6. A method for designing dihedral angle errors of a single corner reflector according to claim 5, characterized in that the transformation matrix between the bottom coordinate system and the cone coordinate system is as follows: 其中为角锥坐标系内的矢量，为底面坐标系内的矢量。in is a vector in the cone coordinate system, is a vector in the base coordinate system. 7.根据权利要求1所述的一种单体角反射器二面角误差的设计方法，其特征在于，构建远场衍射模型的方法还包括：7. The method for designing the dihedral angle error of a single corner reflector according to claim 1, wherein the method for constructing a far-field diffraction model further comprises: 考虑激光偏振特性的远场衍射模拟，具体为：Far-field diffraction simulation considering the polarization characteristics of laser is as follows: 对于偏振光的计算，采用琼斯矢量来描述线偏振光或圆偏振光；对于线偏振光，表示为：θ为线偏振光的偏振角，其大小为线偏振光的偏振方向与坐标系x轴的夹角，对于圆偏振光表示为±分别对应圆偏振光的左旋和右旋；全反射过程仅对s波与p波的相位发生改变，因此，通过一个琼斯矩阵表示这个过程：δs,δp分别表示一次全反射过程中s波与p波的相位变化；For the calculation of polarized light, Jones vector is used to describe linear polarized light or circular polarized light; for linear polarized light, it is expressed as: θ is the polarization angle of linear polarized light, which is the angle between the polarization direction of linear polarized light and the x-axis of the coordinate system. For circular polarized light, it is expressed as ± corresponds to the left and right rotation of circularly polarized light respectively; the total reflection process only changes the phase of the s wave and the p wave, so this process is represented by a Jones matrix: δ s ,δ p represent the phase changes of s-wave and p-wave in a total reflection process respectively; 将所述琼斯矢量和所述琼斯矩阵拓展到三维；Expanding the Jones vector and the Jones matrix to three dimensions; 将激光分解到垂直于入射面与平行于入射面方向，即s波与p波，激光在角反射器内部进行传输，建立坐标系定量描述激光在角反射器内部传输过程中s波与p波的方向与相位的变化；Decompose the laser into directions perpendicular to the incident surface and parallel to the incident surface, namely, s-wave and p-wave. The laser is transmitted inside the corner reflector, and a coordinate system is established to quantitatively describe the changes in the direction and phase of the s-wave and p-wave during the transmission of the laser inside the corner reflector. 对于偏振光，p,s,k构成右手系，且根据s波的物理意义能够得到：For polarized light, p, s, and k form a right-hand system, and according to the physical meaning of s wave, we can get: 其中N表示角反射器入射表面的法线；Where N represents the normal of the incident surface of the corner reflector; 在光线追迹过程中，将光矢量定义在角锥坐标系内；During ray tracing, the light vector is defined in a cone coordinate system; 在应用琼斯矩阵对s波与p波进行相位叠加前，引入一个矩阵来实现坐标系的转换；每次折射或反射过程的菲涅尔公式用一个矩阵表示，第q个表面光矢量发生的变化用矩阵Pq表示：Before applying the Jones matrix to perform phase superposition on the s-wave and the p-wave, a matrix is introduced to realize the conversion of the coordinate system; the Fresnel formula of each refraction or reflection process is represented by a matrix, and the change of the qth surface light vector is represented by the matrix Pq : 由于p,s,k构成右手系，因此矩阵都为正交矩阵，即逆矩阵等于转置矩阵；Jq即表示第q个表面的三维琼斯矩阵；as,q与ap,q分别为s波与p波的透射或反射系数，通过菲涅尔公式计算，具体视发生的光学过程而定；矩阵的用于将角锥坐标系下的光矢量转换到了(sq,pq,kq-1)坐标系下；Oout,q矩阵的作用为将(sq,pq′,kq)坐标系下的光矢量转换到角锥坐标系下；sq表示第q个表面发生折射或反射过程的s波分量；pq表示在第q个表面发生折射或反射过程前的p波分量，通过sq与kq-1叉乘得到；kq-1则表示在角锥坐标系下，第q-1个表面的出射光矢量，kq同理；pq′表示在第q个表面发生折射或反射过程后出射光的p波分量；Since p, s, k form a right-hand system, the matrices are all orthogonal matrices, that is, the inverse matrix is equal to the transposed matrix; J q represents the three-dimensional Jones matrix of the qth surface; a s,q and a p,q are the transmission or reflection coefficients of s-wave and p-wave respectively, calculated by the Fresnel formula, depending on the optical process occurring; The matrix is used to convert the light vector in the pyramid coordinate system to the ( sq , pq , kq-1 ) coordinate system; the function of the Oout ,q matrix is to convert the light vector in the ( sq , pq ′, kq ) coordinate system to the pyramid coordinate system; sq represents the s-wave component of the qth surface refraction or reflection process; pq represents the p-wave component before the qth surface refraction or reflection process occurs, obtained by the cross product of sq and kq-1 ; kq-1 represents the outgoing light vector of the q-1th surface in the pyramid coordinate system, and the same is true for kq ; pq ′ represents the p-wave component of the outgoing light after the qth surface refraction or reflection process occurs; 激光经过角反射器之后的偏振态变化用5个矩阵相乘来描述；5个矩阵分别对应了5次折射或反射过程，将5个矩阵分别记为第一矩阵、第二矩阵、第三矩阵、第四矩阵以及第五矩阵，具体为：The change in polarization state of the laser after passing through the corner reflector is described by multiplying five matrices; the five matrices correspond to five refraction or reflection processes, and the five matrices are recorded as the first matrix, the second matrix, the third matrix, the fourth matrix, and the fifth matrix, specifically: 第一矩阵对应的过程为：激光入射到角反射器底面发生折射；The process corresponding to the first matrix is: the laser is incident on the bottom surface of the corner reflector and refracted; 第二矩阵、第三矩阵、第四矩阵对应的过程为：激光在三个反射面处发生全反射；The processes corresponding to the second matrix, the third matrix, and the fourth matrix are: the laser is totally reflected at three reflection surfaces; 第五矩阵对应的过程为：激光经过底面折射后从角反射器内部向外空间出射；The process corresponding to the fifth matrix is: the laser is refracted by the bottom surface and then emitted from the inside of the corner reflector to the outer space; 整个计算过程为迭代的过程，最初的s0,p0以及p0′的定义为：The entire calculation process is an iterative process. The initial definitions of s 0 , p 0 and p 0 ′ are: p0＝s0×k0 p 0 =s 0 ×k 0 p'0＝s'0×k'0 p' 0 =s' 0 ×k' 0 k′0表示k0经过折射或反射之后的光矢量，以s0,p0以及p0′为基础计算得到5个过程的P矩阵，最终将5个P矩阵相乘再左乘入射偏振矢量得到最终的出射矢量。k′ 0 represents the light vector after k 0 is refracted or reflected. The P matrices of the five processes are calculated based on s 0 , p 0 and p 0 ′. Finally, the five P matrices are multiplied and then left-multiplied by the incident polarization vector to obtain the final output vector. 8.根据权利要求7所述的一种单体角反射器二面角误差的设计方法，其特征在于，激光在角反射器内部传输过程中s波与p波的方向与相位的变化具体为：8. The design method of the dihedral angle error of a single corner reflector according to claim 7, characterized in that the changes in the directions and phases of the s-wave and the p-wave during the transmission of the laser inside the corner reflector are specifically: 激光在角反射器内部传输的过程中，一共会经历两次折射与三次全反射过程；其中，折射仅改变s波与p波的振幅大小，不改变s波与p波的相位；三次全反射过程中，s波与p波的振幅不变，相位发生变化；每次全反射过程中，激光的入射面均不相同，因此s波与p波相位和方向均发生变化。During the transmission of laser light inside the corner reflector, it will undergo two refractions and three total reflections. Refraction only changes the amplitude of the s-wave and p-wave, but does not change the phase of the s-wave and p-wave. During the three total reflections, the amplitude of the s-wave and p-wave remains unchanged, but the phase changes. During each total reflection, the incident surface of the laser is different, so the phase and direction of the s-wave and p-wave change. 9.根据权利要求1所述的一种单体角反射器二面角误差的设计方法，其特征在于，所述角反射器包括实心角反射器和空心角反射器。9. The method for designing the dihedral angle error of a single corner reflector according to claim 1, wherein the corner reflector comprises a solid corner reflector and a hollow corner reflector. 10.根据权利要求1所述的一种单体角反射器二面角误差的设计方法，其特征在于，根据速差角的变化范围内的远场能量分布计算得到最优角反射器二面角误差的方法包括：10. The method for designing the dihedral angle error of a single corner reflector according to claim 1, wherein the method for calculating the optimal dihedral angle error of the corner reflector according to the far-field energy distribution within the range of the speed difference angle comprises: 将速差角的变化范围内的远场能量分布的归一化能量均值作为评价指标得到最优角反射器二面角误差设计。The normalized energy mean of the far-field energy distribution within the range of the speed difference angle is used as the evaluation index to obtain the optimal corner reflector dihedral angle error design.
CN202410936898.7A 2024-07-12 2024-07-12 Design method for dihedral angle errors of single corner reflector Pending CN119001681A (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202410936898.7A CN119001681A (en) 2024-07-12 2024-07-12 Design method for dihedral angle errors of single corner reflector

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202410936898.7A CN119001681A (en) 2024-07-12 2024-07-12 Design method for dihedral angle errors of single corner reflector

Publications (1)

Publication Number Publication Date
CN119001681A true CN119001681A (en) 2024-11-22

Family

ID=93477076

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202410936898.7A Pending CN119001681A (en) 2024-07-12 2024-07-12 Design method for dihedral angle errors of single corner reflector

Country Status (1)

Country Link
CN (1) CN119001681A (en)

Citations (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN105929531A (en) * 2016-07-12 2016-09-07 武汉大学 A Numerical Simulation Method of Far Field Diffraction Intensity of Laser Corner Reflector

Patent Citations (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN105929531A (en) * 2016-07-12 2016-09-07 武汉大学 A Numerical Simulation Method of Far Field Diffraction Intensity of Laser Corner Reflector

Non-Patent Citations (3)

* Cited by examiner, † Cited by third party
Title
周辉, 李松, 石岩, 翁兴涛, 胡克伟: "卫星角反射器的设计", 光电工程, no. 11, 30 November 2005 (2005-11-30) *
周辉;李松;郑国兴;高俊玲;: "卫星角反射器精度对远场衍射模式的影响", 光学学报, no. 01, 15 January 2009 (2009-01-15), pages 61 - 66 *
钟声远;徐广平;吴键;: "卫星激光角反射器的远场衍射光强研究", 激光与红外, no. 02, 15 February 2009 (2009-02-15) *

Similar Documents

Publication Publication Date Title
US4523809A (en) Method and apparatus for generating a structured light beam array
Krist PROPER: an optical propagation library for IDL
CN106444056B (en) Sparse optical synthetic aperture imaging device based on three apertures and light beam combination correction method thereof
CN110954213A (en) Cross-phase-based high-topological-charge-number vortex optical rotation preparation and detection method
JPH0712937A (en) Sequential image composition device
CN113742839B (en) A high-precision modeling method for spacecraft radiation light pressure
Kinoshita et al. Shooting null geodesics into holographic spacetimes
CN105929531B (en) A Numerical Simulation Method of Far Field Diffraction Intensity of Laser Corner Reflector
CN119001681A (en) Design method for dihedral angle errors of single corner reflector
Lohan et al. Characterization of candidate solutions for X-ray pulsar navigation
Gelius Generalized acoustic diffraction tomogra phy 1
Schöller et al. Modeling the imaging process in optical stellar interferometers
Lindlein et al. Design and modeling of a miniature system containing micro-optics
Krist et al. Practical numerical propagation of arbitrary wavefronts through PIAA optics
Barausse The physics of gravitational waves
CN114994909A (en) Off-axis reflection type imaging system design method based on free wave surface control holographic element
Ashcraft et al. Polarization aberrations in next-generation Giant Segmented Mirror Telescopes (GSMTs)-II. Influence of segment-to-segment coating variations on high-contrast imaging and polarimetry
Sokolov A technique for the calculation of the natural waves of a cavity with polarization nonuniform elements
Quadrelli et al. Dynamics and control of granular imaging systems
Pueyo et al. Numerical propagator through PIAA optics
Ashcraft Ray-Based Physical Optics for the Design of Astronomical Observatories
CN116246003B (en) System and method for analyzing initial alignment information of electro-optic modulation equipment
Ryberg A new approach to describe the seismic wavefield using higher order Gaussian beam modes
Dement'ev et al. Fraunhofer diffraction at a nonideal corner reflector with flat faces
Ryberg Seophys. zyxwvutsrqponmlkjihgfed

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination