Microscale six-degree-of-freedom motion measurement method and device based on light intensity distribution model

Abstract

This invention relates to a microscale six-degree-of-freedom motion measurement method and device based on a light intensity distribution model, belonging to the field of precision optical metrology and micro / nano manipulation. The device includes a laser diode and laser coupler, a multi-core optical fiber, a light-modulated target, a multi-channel photodetector, a data acquisition card, and a processor. The multi-core optical fiber consists of a single transmitting fiber and multiple uniformly surrounding receiving fibers. The light-field distribution modulation target has a spatial geometric reflection structure to break the spatial symmetry of the reflected light path. A forward mathematical model is established to describe the nonlinear functional relationship between the six-degree-of-freedom pose of the light-modulated target and multiple independent optical power signals. The six-degree-of-freedom pose is calculated based on the measured optical power values. This invention effectively overcomes the measurement blind zone of traditional fiber optic sensors while maintaining a simple system structure, small size, strong anti-interference capability, and low cost, achieving synchronous, high-precision, and robust measurement of microscale spatial six-degree-of-freedom displacement.

Description

Technical Field

[0001] This invention belongs to the field of precision optical metrology and micro-nano manipulation, and relates to a microscale six-degree-of-freedom motion measurement method and device based on a light intensity distribution model, specifically a microscale six-degree-of-freedom motion measurement method and device based on a geometric optical light intensity distribution model. Background Technology

[0002] With the rapid development of advanced manufacturing, micro-nano robotics, microelectromechanical systems, and precision optics, the demand for precise measurement and control of spatial motion at the micrometer and even nanometer scale is becoming increasingly urgent. Six degrees of freedom (6-DOF) measurement involves simultaneously acquiring the three translational axes of an object in space. and three rotation axes Position and pose information is a key technology for achieving high-precision positioning, assembly, control, and calibration.

[0003] Existing six-degree-of-freedom (6DOF) measurement technologies mainly include laser interferometers, machine vision systems, and capacitive / inductive sensors. While laser interferometers can provide sub-nanometer-level single-axis measurement resolution, achieving 6-DOF measurement requires constructing a complex multi-optical-path system. This not only results in high equipment costs and large size but also places extremely high demands on optical path collimation and environmental stability, making it susceptible to interference from cross-axis coupling effects. In microscale applications, machine vision systems are often limited by the depth of field of the microscope lens, resulting in a limited measurement range. This makes it difficult to simultaneously guarantee high resolution and a large measurement range, and thus difficult to achieve full 6-DOF dynamic tracking.

[0004] In recent years, fiber optic sensing technology has shown great potential in the field of displacement measurement due to its unique advantages such as small size, low cost, resistance to electromagnetic interference, and ability to perform remote measurements. For example, Chinese invention patent CN106338250B discloses a scanning method for a scanning optical displacement sensor. By driving a piezoelectric ceramic tube to move an optical fiber cantilever beam, the scanning range is expanded and the topographic features of the object being measured can be obtained. However, this device introduces mechanical vibration components, which reduces the dynamic response frequency of the system. Moreover, the scanning method is essentially a time-division measurement, which cannot meet the requirements of real-time, synchronous, and high-bandwidth detection of six degrees of freedom pose in micro-nano manipulation. For example, Chinese invention patent CN119509373B discloses a reflective optical displacement sensor and its usage. Through a dual-receiving optical fiber structure design and differential algorithm, the influence of light source fluctuation and light bending loss is eliminated, improving the stability of axial displacement measurement. However, it is still essentially a one-dimensional displacement sensor. Due to the light field symmetry of the plane reflector, this structure cannot sense the lateral translation along the X and Y axes and the rotation around the axis of the measured object, resulting in a significant measurement blind zone and the inability to achieve multi-degree-of-freedom decoupling.

[0005] In summary, traditional fiber optic displacement sensors primarily use planar mirrors as targets. Limited by the axisymmetry of the planar optical field, the system is insensitive to lateral translation and rotation around the optical axis, making 6-DOF decoupled measurement impossible. While laser interferometers offer high precision, their complex optical paths, large size, and high cost make them difficult to integrate into space-constrained environments such as micro-nano manipulation. Machine vision systems, on the other hand, are limited by the depth-of-field constraints of the microscope lens, making it difficult to simultaneously achieve high resolution and large-scale dynamic tracking. This invention provides a microscale six-DOF motion measurement method and device based on a light intensity distribution model. By using a centrally transmitting, surround-receiving fiber optic probe in conjunction with a light-modulated target, and utilizing the light intensity distribution model for decoupling, high-precision, non-contact, synchronous measurement of spatial pose (6-DOF) is achieved. Summary of the Invention

[0006] To address the fundamental limitations of existing technologies, such as the insensitivity to lateral translation and rotation around the optical axis in traditional fiber optic displacement sensors using planar mirrors as targets, which prevent full six-degree-of-freedom (6DOF) measurement, and the application bottlenecks of existing 6-DOF technologies like laser interferometers and visual measurement, including system complexity, high cost, large size, and susceptibility to environmental interference, this invention provides a microscale six-DOF motion measurement method and device based on a light intensity distribution model. Specifically, it is a microscale six-DOF motion measurement method and device based on a geometric optics light intensity distribution model. This invention constructs a non-contact sensing optical path composed of a multi-core optical fiber and a target with light field distribution modulation, overcoming the symmetry limitation of light field reflection by traditional planar mirrors. This invention establishes and solves a unified forward mathematical model based on geometric optics light intensity distribution, achieving precise decoupling of six highly coupled light intensity signals. Through dual innovations in structure and algorithm, this invention effectively overcomes the measurement blind zone of traditional fiber optic sensors while maintaining a simple system structure, small size, strong anti-interference capability, and low cost, achieving microscale spatial six-DOF displacement measurement. Its synchronous, high-precision, and robust measurements precisely meet the urgent needs of cutting-edge fields such as advanced manufacturing, micro-nano manipulation, and microelectromechanical systems for precision motion calibration.

[0007] To achieve the above objectives, the technical solution adopted by the present invention is as follows: A microscale six-degree-of-freedom motion measurement device based on a light intensity distribution model is described. The device includes a laser diode and laser coupler, a multi-core optical fiber, a light-modulated target, a multi-channel photodetector, a data acquisition card, and a processor. The laser diode and laser coupler serve as the light source system for the entire measurement device. They are connected to the transmitting fiber in the multi-core optical fiber via fiber optic connectors to provide the required light beam for measurement. The multi-core optical fiber, as the core component for beam transmission and spatial sampling, employs a central transmitting and surrounding receiving arrangement at its probe end face. The central transmitting fiber is used for... A light beam provided by a laser diode and laser coupler is projected onto an optically modulated target. N receiving fibers, connected to a multi-channel photodetector, are evenly distributed around the transmitting fiber. The optically modulated target is positioned directly in front of the end face of the multi-core fiber common probe. When the optically modulated target undergoes a six-degree-of-freedom pose change with the object under test, its multi-faceted pyramidal reflection structure, composed of multiple planar reflective units circumferentially distributed around a central axis and sharing a common convergence vertex and preset tilt angle, modulates the received initial light beam. The light spot reflected back to the end face of the multi-core fiber common probe forms a specific light intensity distribution that dynamically changes with the pose, breaking the symmetry of the light field reflected by traditional plane mirrors. The multi-channel photodetector synchronously converts the N optical power signals into analog electrical signals, which are then converted from analog to digital by a data acquisition card and uploaded to a processor. The processor runs a forward mathematical model based on geometric optics light intensity distribution and uses an iterative optimization algorithm to precisely decouple the highly coupled analog electrical signals, ultimately outputting the six-degree-of-freedom pose parameters of the optically modulated target relative to the multi-core fiber.

[0008] Furthermore, the end face of the receiving optical fiber is flush with the end face of the probe of the multi-core optical fiber, and the reflected light spot is spatially sampled in its respective determined core aperture area to capture a portion of the energy of the light field distribution. The captured N independent optical power signals are transmitted to the multi-channel photodetector at the back end through the multi-core optical fiber.

[0009] Furthermore, the laser diode and laser coupler consist of two parts: a laser diode and a laser coupler. The laser diode is used to generate an initial beam, which is then fed into the laser coupler. The coupled laser beam after passing through the laser coupler is efficiently and stably guided into the core of the transmitting optical fiber.

[0010] Furthermore, the internal structure of the multi-core optical fiber encapsulates and integrates one transmitting fiber and at least one receiving fiber, i.e., N≥1. The transmitting fiber is located at the center of the end face of the multi-core optical fiber probe. The receiving fibers are located around the transmitting fiber, each receiving fiber having a defined core radius, and each receiving fiber constitutes an independent light intensity extraction channel. By capturing the light intensity of the reflected light field at different spatial locations, the six-degree-of-freedom pose change of the object under test is encoded into a multi-path parallel optical power signal. All the fibers included in the multi-core optical fiber, i.e., the transmitting fiber and the receiving fiber, have specific numerical aperture characteristics. These numerical aperture characteristics are used to limit the divergence angle of the transmitted beam and the effective fiber receiving cone angle of the receiving fiber.

[0011] Furthermore, if the number of receiving optical fibers is two or more, i.e., N≥2, they are uniformly distributed around the transmitting optical fiber, thereby constructing a discrete spatial sampling array on the end face of the multi-core optical fiber. The overall multi-core optical fiber adopts a fan-out fiber bundle structure, which is physically composed of a common probe end and discrete connection ends.

[0012] Furthermore, the optical modulation target is a reflective component with a preset spatial geometry, configured to break the spatial symmetry of the reflected light field to encode its six-degree-of-freedom pose changes as changes in the reflected light intensity distribution. Specifically, the optical modulation target includes K planar reflective units circumferentially distributed around a central axis; the K planar reflective units share a common geometric convergence vertex in space, and the mirror normal vector of each planar reflective unit forms a preset non-zero tilt angle with the central axis of the optical modulation target. Further, the optical modulation target includes K geometric corner points located at the peripheral geometric vertices of the front-end planar reflective units, collectively defining the outer contour boundary of the effective reflection area of ​​the optical modulation target. Through the above construction, the optical modulation target as a whole forms a K-faceted angular pyramidal mirror structure with a central concave or convex shape (preferably a centrally concave inner pyramidal structure). When the incident light beam illuminates the target, different planar reflecting units split the beam and reflect it to different spatial regions. When the target undergoes translational or rotational motion, the energy distribution of the light spot on the end face of the multi-core fiber optic common probe will undergo specific nonlinear changes due to the geometric projection changes of each planar reflecting unit. A global coordinate system is established using the right-hand coordinate system rule. The origin O of the global coordinate system is located at the center of the end face of the multi-core fiber optic probe, that is, at the intersection of the axis of the transmitting fiber core and this end face. The Z-axis coincides with the axis of the transmitting fiber core, and its positive direction is defined as the emission direction of the light, that is, the direction perpendicular from the end face of the transmitting fiber to the target. The Y-axis is located on the end face of the transmitting fiber, and its positive direction is defined as the direction from the origin O to the center of the multi-core fiber core. The X-axis is determined by the right-hand coordinate system rule and is also located on the end face of the common probe of the multi-core fiber optic probe. Furthermore, in order to accurately describe the six degrees of freedom motion of the optically modulated target relative to the multi-core fiber, this invention establishes a target coordinate system fixed to the optically modulated target. The origin O' is defined as the common geometric convergence vertex of all planar reflective units of the optical modulation target. A zero-pose state is defined: in this zero-pose state, the optical modulation target does not rotate, and its origin O' is located on the Z-axis of the global coordinate system. The Z' axis is defined as the principal axis of the target coordinate system. In the zero-pose state, the Z' axis is parallel and in the same direction as the Z-axis of the global coordinate system. The Y' axis is defined as parallel and in the same direction as the Y-axis of the global coordinate system in the zero-pose state. The X' axis is determined according to the right-hand rule of the coordinate system. In the zero-pose state, the X' axis is parallel and in the same direction as the X-axis of the global coordinate system. The optical modulation target is spatially arranged directly in front of the end face of the multi-core optical fiber and separated from the end face of the multi-core optical fiber by a working distance along the Z-axis direction of the global coordinate system to receive the initial beam from the transmitting fiber. During the measurement process, the optical modulation target is rigidly fixed to the surface of the object under test through a base, thereby ensuring that it maintains a synchronous motion state with the object under test. Therefore, the microscale six-degree-of-freedom motion measurement device can accurately characterize the spatial motion trajectory and attitude changes of the object under test by measuring the six-degree-of-freedom pose change of the optically modulated target relative to the multi-core optical fiber in real time.

[0013] Furthermore, the reflected light spot formed by the backlight beam emitted by the transmitting fiber and reflected by the optical modulation target has a specific reflected light intensity distribution that dynamically changes with the orientation of the optical modulation target on the end face of the multi-core fiber. The multiple receiving fibers located on the end face of the common probe of the multi-core fiber spatially sample the reflected light spot in their respective fiber core aperture areas, capturing a portion of the light energy of the reflected light intensity distribution.

[0014] Furthermore, the multi-channel photodetector is located at the end of the multi-core optical fiber, specifically, the receiving fiber probe in the separate connection end of the multi-core optical fiber is connected one-to-one with each of the N photoelectric sensing channels of the multi-channel photodetector; the N photoelectric sensing channels of the multi-channel photodetector serve as its input terminals. The multi-channel photodetector is configured as a photoelectric conversion module, its core function being to convert the six independent optical power signals transmitted from the receiving fiber in real time and synchronously. to These signals are converted into N corresponding analog electrical signals, and the amplitude of these N analog electrical signals represents the real-time light intensity received by the N receiving optical fibers.

[0015] Furthermore, the input terminal of the data acquisition card is connected to the output terminal of the multi-channel photodetector, and it is configured as a signal acquisition and conversion module to receive multiple analog electrical signals output by the multi-channel photodetector and convert them into digital signals.

[0016] Furthermore, the processor is communicatively connected to the data acquisition card and is configured as the core of the entire device's computation and control. The processor receives digital signals from the data acquisition card and processes these signals using a preset light intensity distribution model and pose calculation algorithm, thereby calculating the six-degree-of-freedom pose parameters of the optically modulated target relative to the multi-core optical fiber in real time.

[0017] This invention establishes a unified, forward mathematical model based on geometric optics and the light intensity distribution characteristics of a preset light source. The computational flow of this forward mathematical model encompasses the following core steps: First, based on the input light modulation target pose parameters, the normal vector and spatial equation of each planar reflector unit in the global coordinate system are calculated in real time using a homogeneous coordinate transformation matrix. Then, based on the geometric optics reflection imaging principle, the virtual image point coordinates of the light source with respect to each planar reflector unit are derived, and the effective illumination area of ​​the reflected beam on the end face of the multi-core fiber common probe is defined accordingly. The virtual image point coordinates are substituted into the preset Gaussian beam intensity distribution equation to construct an instantaneous radiation intensity distribution model at any sampling point on the end face of the multi-core fiber common probe. Finally, by performing a double integral on the light intensity distribution at the geometric intersection of the effective illumination area and the aperture areas of each receiving fiber core, the theoretically required coupled optical power value to be captured by the N receiving fibers is calculated. to Specifically, it includes the following steps: The first step is to process the known pose parameters of the optically modulated target using the homogeneous coordinate transformation principle to obtain the target coordinate system. In the global coordinate system The homogeneous matrix of attitude and position in the target coordinate system is obtained; the homogeneous matrix is ​​then processed by homogeneous coordinate transformation with any point in the target coordinate system and the mirror normal vector to obtain the global coordinate system. Given any point in the coordinate system and the normal vectors of each mirror; based on the global coordinate system... The normal vectors of each mirror surface and their common converging vertex are used to determine the deterministic equations of each planar reflection unit in the current pose. Specifically: Step 1.1: Based on the known six-degree-of-freedom pose parameters of the optical modulation target relative to the global coordinate system of the multi-core fiber common probe end face. ,in, This represents the lateral translation of the optically modulated target along the X-axis of the global coordinate system. This represents the lateral translation of the optically modulated target along the Y-axis of the global coordinate system. This represents the lateral translation of the optically modulated target along the Z-axis of the global coordinate system. This represents the pitch angle of the optically modulated target rotating about the X-axis of the global coordinate system. This represents the pitch angle of the optically modulated target rotating about the Y-axis of the global coordinate system. This represents the pitch angle of the optically modulated target rotating around the Z-axis of the global coordinate system; the six-degree-of-freedom pose parameters are processed using the homogeneous coordinate transformation principle, i.e., a homogeneous matrix is ​​introduced. Describe the target coordinate system In the global coordinate system The posture and position in the middle: (1) in, The relative pose of the optically modulated target with respect to the end face of the multi-core fiber common probe is the input target coordinate system. In the global coordinate system The pose parameters are as follows; A homogeneous matrix representing the attitude and position of the target coordinate system in the global coordinate system.

[0018] Step 1.2 describes the transformation of any point and normal vector in the target coordinate system into the global coordinate system. This is done using the homogeneous matrix obtained in Step 1.1. The transformation of the homogeneous coordinates of any point in the target coordinate system and the mirror normal vector to the global coordinate system can be further described as follows: (2) in, and These represent the representations of any point in space in the global coordinate system and the target coordinate system, respectively. and These represent the normal vectors of each mirror surface of the optically modulated target in the global coordinate system and the target coordinate system, respectively.

[0019] Assume that the K planar reflective units of the optically modulated target are all ideal planes, and they intersect at a point in the global coordinate system. Each planar reflecting unit can be described by the following deterministic equation: (3) in, The first term represents the optical modulation target. One planar reflective unit, of which The range is from 1 to K; Indicates the first The projection components of the normal vectors of each plane onto the X-axis of the global coordinate system. This represents the projection component on the Y-axis. Represents the projection components on the Z-axis, and the combination of the three is the first. Normal vectors of the planes , ; This represents the coordinate value of any point on the plane on the X-axis of the global coordinate system. This represents the coordinate value on the Y-axis. This represents the coordinate value on the Z-axis; the combination of the three values ​​is the first... An interior point on a plane , ; This represents the lateral translation of the optically modulated target along the X-axis of the global coordinate system. This represents the lateral translation of the optically modulated target along the Y-axis of the global coordinate system. This represents the lateral translation of the optically modulated target along the Z-axis of the global coordinate system; the combination of these three factors constitutes the common convergence vertex of all the planar reflective units. O ,Right now ; The second step involves processing the spatial sampling points on the end face of the multi-core fiber optic common probe and the deterministic equations of each planar reflection unit determined in the first step using a virtual image point mapping model to calculate the virtual image point coordinates of the sampling points with respect to each planar reflection unit. The geometric corner points and virtual image point coordinates of the optical modulation target are then processed using ray tracing and geometric projection methods to determine the effective illumination area of ​​the reflected beam on the end face of the multi-core fiber optic common probe. First, a virtual image point mapping model is constructed to solve for the spatial midpoint. Relative to each planar reflection unit virtual image points Subsequently, all geometric corner points of the optical modulation target are processed using a virtual image point mapping model to obtain all projected boundary points on the end face of the multi-core fiber. The topological boundaries of all these projected boundary points are then connected and region closure is performed, ultimately defining and obtaining the effective illumination area corresponding to the reflected beam on the end face of the multi-core fiber. Specifically: Step 2.1: Construct a virtual image point mapping model to solve for the midpoint in space. Relative to each planar reflection unit virtual image points Specifically: vector ,and In the normal vector Projection on Described as: (4) therefore, Q Point on a plane Projection on Represented as: (5) and Q Virtual image of a point Based on the virtual pixel mapping model, the following formula can be derived: (6) The virtual image point Calculated using the following formula: (7) (8) (9) in, , , These respectively represent the calculated virtual image points. Coordinate components on the X, Y, and Z axes of the global coordinate system. , , These represent the coordinate components of any point in space whose image is to be obtained, located on the X, Y, and Z axes of the global coordinate system, respectively. , , and , , The meaning is the same as the definition in the aforementioned plane equation.

[0020] Step 2.2: Repeat the virtual image point mapping model described in Step 2.1 for all peripheral geometric corner points of the optical modulation target to obtain all projected boundary points on the multi-core fiber end face. Perform topological boundary connection and region closure processing on all projected boundary points to finally define and obtain the effective illumination area corresponding to the reflected beam on the multi-core fiber end face. Specifically: The geometric features of the optically modulated target are defined as key corner points in the global coordinate system: the Mth geometric corner point and the central convergence point are represented in the target coordinate system as follows: as well as Its coordinate transformation in the target coordinate system using a homogeneous matrix results in its representation in the global coordinate system. and a central convergence point To determine the above geometric corner points The corresponding projection boundary point on the end face of the multi-core fiber common probe The virtual image point mapping model established in step 2.1 is used for joint solution, specifically: First, calculate the light source point. L Passing through geometric corners The ray and the multi-core fiber common probe end face reflect each other about the plane of the geometric corner point M. The virtual intersection point of the virtual mirror plane. According to geometric relationships, this virtual intersection point lies on the ray. Above, satisfying the ray equation: (10) in: , , These represent the geometric corners through which the light source point passes. The virtual intersection point of the ray and the virtual mirror plane of the multi-core fiber common probe end face about the geometric corner point M in the plane reflection unit. Coordinate components on the X, Y, and Z axes of the global coordinate system; Represents the geometric corners of the optically modulated target. Coordinate vector in the global coordinate system; Represents the scaling parameters of the ray equation; This indicates the direction from the light source point L to the geometric corner point. The direction vector.

[0021] At the same time, this virtual intersection Z-axis component Determined by the geometric intercept of each planar reflection unit, the result is obtained using a virtual image point mapping model: (11) Solve the parameters simultaneously Then, determine the virtual intersection point. Complete coordinates, then Derived from the following formula: (12) (13) in: , Representing geometric corner points After the first After reflection by each planar reflector unit, the projected boundary points on the end face of the multi-core fiber common probe are... Coordinate components on the X and Y axes of the global coordinate system; This represents the projection component of the plane's normal vector onto the X-axis of the global coordinate system. This represents the projection component on the Y-axis. Represents the projection components on the Z-axis, and the combination of the three is the first. Normal vectors of the planes , ; , , The meaning is the same as the previous definition, representing the coordinate components of the common converging vertices.

[0022] Repeat the above calculation for all geometric corner points to obtain K projected vertices on the end face of the multi-core fiber common probe. to Based on the topological connections of these vertices, the effective illumination area corresponding to each planar reflective unit on the end face of the multi-core fiber common probe is obtained. The core of this step lies in establishing a mathematical mapping of the reflection process through geometric transformation. The virtual image point refers to the virtual source point emitted from a symmetrical position behind the mirror, which is equivalent to the back light beam reflected by each planar reflection unit of the light modulation target based on the plane reflection law; the effective illumination area refers to the actual spot coverage area projected onto the end face of the multi-core fiber common probe after being modulated and reflected by the light modulation target.

[0023] The third step, based on the effective illumination area determined in the second step, involves the processor calculating the sampling point on the end face of the multi-core fiber optic common probe. The light intensity distribution function at that location. Specifically, according to the principle of geometrical optics reflection imaging, the light intensity received by the sampling point located on the end face of the multi-core fiber is the light intensity distribution function after passing through the first... The intensity of light reflected from a plane is physically equivalent to the intensity of the initial beam of light that, without reflection, propagated directly to that point with respect to the plane. The light intensity at the virtual image point. Specifically: First, the processor maps the sampling points on the end face of the multi-core fiber common probe according to the virtual image point mapping model constructed in step 2.1. Substituting the global coordinates, the coordinate components of the corresponding virtual image point in the global coordinate system are calculated as follows: (14) (15) (16) in: The first term represents the optical modulation target. There are planes, among which The range is from 1 to K; The calculated coordinate components of the virtual image point on the X-axis of the global coordinate system represent the coordinate components of the virtual image point. Represents the coordinate components on the Y-axis. The three components, representing the coordinates on the Z-axis, are combined to form the virtual image point. ; This represents the projection component of the plane's normal vector onto the X-axis of the global coordinate system. This represents the projection component on the Y-axis. Represents the projection components on the Z-axis, and the combination of the three is the first. Normal vectors of the planes ; This represents the coordinates of the convergent vertex of all planar reflection units on the X-axis of the global coordinate system. This represents the coordinate value on the Y-axis. These represent the coordinate values ​​on the Z-axis; the combination of these three values ​​constitutes the common converging vertex. O ,Right now ; This indicates a sampling point on the end face of a multi-core fiber optic common probe. Projection components on the X-axis of the global coordinate system This represents the coordinate value on the Y-axis. The point lies in the XY plane of the global coordinate system, therefore the combination of the two forms the... .

[0024] The processor will virtual pixels Substituting into the Gaussian beam intensity distribution equation, calculate the virtual image point. Light intensity distribution function : (17) in, For virtual image points The radiation intensity at that location, The intensity is the central light intensity at the waist of the beam, which is the maximum intensity at the start of the beam propagation. The waist radius is the radius of the beam at its narrowest point. The distance between the waist and the Z-axis direction The beam radius at that location is calculated using the following formula: ,in The Rayleigh length is calculated using the following formula: , The wavelength of the laser. , , For virtual image points The X, Y, and Z coordinate components in the global coordinate system. Similarly, when using other light beams, simply replace the corresponding intensity distribution function.

[0025] The fourth step involves integrating and superimposing the received fiber-coupled optical power. This is based on the solution obtained in the third step regarding the virtual image points. The processor, combining the light intensity distribution function with the physical structure parameters of the multi-core optical fiber, numerically integrates the actual optical power captured by the N receiving optical fibers to solve for the light intensity distribution function. Specifically: The acquisition of optical signals by a multi-channel photodetector is mathematically equivalent to integrating the light intensity within the effective aperture of the receiving fiber core. The domain of the integration interval depends on the intersection of the effective illumination region and the effective aperture region of the receiving fiber. One planar reflective unit Reflected and by the first The optical power captured by a receiving optical fiber is defined as optical intensity. The double integral over the intersection of the effective illumination area and the receiving fiber core area is calculated using the following formula: (18) Since the optically modulated target contains K planar reflective units, the first... The total optical power output by the receiving optical fiber is the linear superposition of the component optical powers contributed by the K planar reflecting units. The specific calculation formula is as follows: (19) (20) in, Indicates the first The root receiving fiber from the first The component light power received by each planar reflector unit; Indicates by the first The effective lighting area generated by each planar reflective unit; Indicates the first The core aperture region of the receiving optical fiber; This represents the geometric intersection of two regions; , , Coordinates of the end face of the multi-core fiber optic common probe Corresponding virtual image points The coordinate components in the global coordinate system have values ​​that vary with the integration position. Change with change; Indicates the first The total theoretical optical power output from the receiving fiber is the final output of the forward mathematical model. This value is used to compare the residuals of the signals actually collected by the multi-channel photodetector in order to achieve reverse pose optimization solution.

[0026] The beneficial effects of this invention are as follows: (1) The microscale six-degree-of-freedom motion measurement device designed in this invention utilizes the synergistic cooperation between a multi-core fiber optic probe and a light-modulated target to spatially modulate the light field using the specific reflection structure of the target. This breaks the symmetry limitation of the light field reflected by traditional plane mirrors and effectively solves the problem of traditional fiber optic sensors being insensitive to lateral translation and rotation around the optical axis, thereby acquiring full-dimensional pose change information. Furthermore, compared to traditional measurement devices such as laser interferometers, this device has advantages such as compact structure, high integration, and strong anti-electromagnetic interference capability, making it easy to integrate and apply in space-constrained or complex electromagnetic environments such as micro-nano manipulation platforms.

[0027] (2) The measurement method designed in this invention can be adapted to the measurement device designed in this invention. By establishing a forward mathematical model based on geometric optics and Gaussian beams, it can characterize the nonlinear coupling relationship between the optically modulated target pose and the multi-channel optical signal, thereby helping to achieve accurate decoupling and inverse solution of the six-degree-of-freedom pose parameters. In addition, the use of a laser light source combined with a non-contact measurement method is beneficial to eliminating the interference of mechanical contact with the small object under test, and can improve the signal stability and signal-to-noise ratio of the measurement system to a certain extent. Attached Figure Description

[0028] Figure 1 This is an application example diagram of the six-degree-of-freedom motion measurement device in the embodiments of the present invention; Figure 2 This is a flowchart illustrating the signal transmission process of the six-degree-of-freedom motion measurement device in an embodiment of the present invention. Figure 3 This is a schematic diagram showing the relative pose of the common probe end of the multi-core optical fiber 20 and the optical modulation target 30 in an embodiment of the present invention; Figure 4 This is a schematic diagram of the common probe end face structure of the multi-core optical fiber 20 in an embodiment of the present invention; Figure 5 This is a schematic diagram of the planar reflective unit layout of the optical modulation target 30 in an embodiment of the present invention; Figure 6 This is a schematic diagram of the geometric optical reflection imaging principle based on virtual image points in an embodiment of the present invention.

[0029] In the diagram: 10 laser diodes and laser couplers; 20 multi-core optical fibers; 30 optically modulated target; 40 multi-channel photodetectors; 50 data acquisition cards; 60 processors; 21 First receiving optical fiber; 22 Second receiving optical fiber; 23 Third receiving optical fiber; 24 Fourth receiving optical fiber; 25 Fifth receiving optical fiber; 26 Sixth receiving optical fiber; 27 Transmitting optical fiber.

[0030] 31 First planar reflection unit; 32 Second planar reflection unit; 33 Third planar reflection unit; 34 Fourth planar reflection unit. Detailed Implementation

[0031] To make the problem solved by the present invention, the method adopted, and the effect achieved by the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. The derivation and calculation process of the mathematical model of the present invention will be explained in detail using a Gaussian beam as a typical example of a light source. However, it should be understood that those skilled in the art can replace the Gaussian function in the following derivation with other light intensity distribution functions, which also fall within the scope of protection of the present invention.

[0032] An application example diagram of the six-degree-of-freedom motion measurement device in this invention is shown in the embodiment diagram. Figure 1 As shown: The multi-core fiber microscale six-degree-of-freedom motion measurement device includes a laser diode and laser coupler 10, a multi-core fiber 20, an optically modulated target 30, a multi-channel photodetector 40, a data acquisition card 50, and a processor 60; the laser diode and laser coupler 10 is configured as the light source system of the entire measurement device. In this embodiment, the signal transmission flowchart of the device is as follows. Figure 2As shown: The laser diode and laser coupler 10 are connected to the transmitting fiber 27 in the multi-core optical fiber 20 via an optical fiber connector, providing the beam required for measurement to the transmitting fiber 27; the laser diode and laser coupler 10 are configured as the light source system of the entire measurement device, and are connected to the transmitting fiber 27 in the multi-core optical fiber 20 via an optical fiber connector, providing the beam required for measurement to the transmitting fiber 27; the multi-core optical fiber 20 is the core component for beam transmission and spatial sampling, and its probe end face adopts a central emission and surrounding reception arrangement structure. The central transmitting fiber 27 is responsible for projecting the beam provided by the laser diode and laser coupler 10 onto the optical modulation target 30. N receiving fibers are evenly distributed around the transmitting fiber 27, and the end faces of the N receiving fibers are flush with the probe end face of the multi-core optical fiber 20, and each of them performs spatial sampling of the reflected light spot within its respective determined core aperture area, capturing a portion of the energy of the light field distribution. The captured N independent optical power signals are transmitted to the multi-channel photodetector 40 at the back end through the multi-core optical fiber 20. The optical modulation target 30 is positioned directly in front of the common probe end face of the multi-core optical fiber 20. When the optical modulation target 30 undergoes a six-degree-of-freedom pose change with the object under test, its multi-faceted pyramidal reflection structure, composed of multiple planar reflection units circumferentially distributed around the central axis and sharing a common convergence vertex and a preset tilt angle, modulates the received initial light beam. The light spot reflected back to the common probe end face of the multi-core optical fiber 20 forms a specific light intensity distribution that dynamically changes with the pose, breaking the symmetry of the light field reflected by traditional plane mirrors. The multi-channel photodetector 40 synchronously converts the N optical power signals into analog electrical signals, which are then converted from analog to digital by the data acquisition card 50 and uploaded to the processor 60. The processor 60 runs a forward mathematical model based on the geometric optics light intensity distribution and uses an iterative optimization algorithm to precisely decouple the highly coupled analog electrical signals, ultimately outputting the six-degree-of-freedom pose parameters of the optical modulation target 30 relative to the multi-core optical fiber 20.

[0033] Furthermore, the end face of the receiving optical fiber is flush with the probe end face of the multi-core optical fiber 20, and spatial sampling is performed on the reflected light spot within its respective determined core aperture area to capture a portion of the energy of the light field distribution. The captured N independent optical power signals are transmitted to the multi-channel photodetector 40 at the back end through the multi-core optical fiber 20.

[0034] Furthermore, the laser diode and laser coupler 10 consists of two parts: a laser diode and a laser coupler. The laser diode generates an initial light beam, which is then fed into the laser coupler. The laser beam is efficiently and stably guided into the core of the transmitting fiber 27 through the coupling of the laser coupler. Specifically, in this embodiment, the laser diode in the laser diode and laser coupler 10 is preferably a laser diode with a center wavelength of 660nm. The 660nm initial light beam generated by the laser diode is fed into the laser coupler, which is used to efficiently and stably guide the light beam into the core of the transmitting fiber 27.

[0035] Furthermore, the internal structure of the multi-core optical fiber 20 encapsulates and integrates a transmitting optical fiber 27 and at least one receiving optical fiber, i.e., N≥1. The transmitting optical fiber 27 is located at the center of the probe end face of the multi-core optical fiber 20. The receiving optical fibers are located around the transmitting optical fiber 27, each receiving optical fiber has a defined core radius, and each receiving optical fiber constitutes an independent light intensity extraction channel. By capturing the light intensity of the reflected light field at different spatial locations, the six-degree-of-freedom pose change of the object under test is encoded into a multi-channel parallel optical power signal. All the optical fibers included in the multi-core optical fiber 20, i.e., the transmitting optical fiber 27 and the receiving optical fiber, have specific numerical aperture characteristics. These numerical aperture characteristics are used to limit the divergence angle of the emitted beam and the effective fiber receiving cone angle of the receiving optical fiber.

[0036] Furthermore, if the number of receiving optical fibers is two or more, i.e., N≥2, they are uniformly distributed around the transmitting optical fiber 27, thereby constructing a discrete spatial sampling array on the end face of the multi-core optical fiber 20. The overall multi-core optical fiber 20 adopts a fan-out fiber bundle structure, physically consisting of a common probe end and discrete connection ends. In a preferred embodiment of the present invention, six receiving optical fibers 21-26 are used, each receiving optical fiber having a defined core radius. All optical fibers included in the multi-core optical fiber 20, i.e., the transmitting optical fiber 27 and the receiving optical fibers 21-26, have specific numerical apertures. In an embodiment of the present invention, a schematic diagram of the end face structure of the common probe end of the multi-core optical fiber 20 is shown below. Figure 4 As shown, in this embodiment, the multi-core optical fiber 20 includes a transmitting optical fiber 27 and a first receiving optical fiber 21, a second receiving optical fiber 22, a third receiving optical fiber 23, a fourth receiving optical fiber 24, a fifth receiving optical fiber 25, and a sixth receiving optical fiber 26 uniformly distributed around the transmitting optical fiber 27. Furthermore, the multi-core optical fiber 20 adopts a fan-out optical fiber bundle structure, physically consisting of a common probe end and discrete connection ends.

[0037] Furthermore, the light modulation target 30 is a reflective component with a preset spatial geometry, configured to break the spatial symmetry of the reflected light field to encode its six-degree-of-freedom pose changes as changes in the reflected light intensity distribution. Specifically, the light modulation target 30 includes K planar reflective units circumferentially distributed around a central axis; the K planar reflective units have a common geometric convergence vertex in space, and the mirror normal vector of each planar reflective unit forms a preset non-zero tilt angle with the central axis of the light modulation target 30. Further, the light modulation target 30 includes K geometric corner points located at the peripheral geometric vertices of the front-end planar reflective units, collectively defining the outer contour boundary of the effective reflection area of ​​the light modulation target 30. Through the above construction, the light modulation target 30 as a whole forms a K-faceted angular pyramidal mirror structure with a central concave or convex shape (preferably a centrally concave inner pyramidal structure). In a preferred embodiment of the present invention, the light modulation target 30 adopts a four-sided hollow corner pyramidal mirror structure, which is precisely assembled from four independent planar reflective units. These four planar reflective units have a common converging vertex. A schematic diagram of the planar reflective unit layout of the light modulation target 30 is shown below. Figure 5 As shown, it consists of a first planar reflection unit 31, a second planar reflection unit 32, a third planar reflection unit 33, and a fourth planar reflection unit 34. A schematic diagram of the relative pose between the common probe end of the multi-core optical fiber 20 and the optical modulation target 30 is shown below. Figure 3 As shown, when the incident light beam is irradiated by the multi-core fiber 20 onto the optically modulated target 30, different planar reflector units split the beam and reflect it to different spatial regions. When the target undergoes translational or rotational motion, the energy distribution of the light spot on the common probe end face of the multi-core fiber 20 will undergo specific nonlinear changes due to the geometric projection changes of each planar reflector unit. A global coordinate system is established using the right-hand coordinate system rule. The origin O of the global coordinate system is located at the center of the end face of the multi-core fiber 20 probe, that is, at the intersection of the axis of the core of the transmitting fiber 27 and this end face. The Z-axis coincides with the core axis of the transmitting fiber 27, and its positive direction is defined as the emission direction of the light, that is, the direction perpendicular from the end face of the transmitting fiber 27 to the target. The Y-axis is located on the end face of the transmitting fiber 27, and its positive direction is defined as the direction from the origin O to the core center of the multi-core fiber 20. The X-axis is determined by the right-hand coordinate system rule and is also located on the end face of the common probe of the multi-core fiber 20. Furthermore, in order to accurately describe the six degrees of freedom motion of the optical modulation target 30 relative to the multi-core fiber 20, this invention establishes a target coordinate system fixed to the optical modulation target 30. The origin O' is defined as the common geometric convergence vertex of all planar reflective units of the optical modulation target 30. A zero pose state is defined: in this zero pose state, the optical modulation target 30 does not rotate, and its origin O' is located on the Z-axis of the global coordinate system. The Z' axis is defined as the principal axis of the target coordinate system. In the zero pose state, the Z' axis is parallel and in the same direction as the Z-axis of the global coordinate system. The Y' axis is defined as parallel and in the same direction as the Y-axis of the global coordinate system in the zero pose state. The X' axis is determined according to the right-hand rule of the coordinate system. In the zero pose state, the X' axis is parallel and in the same direction as the X-axis of the global coordinate system. The optical modulation target 30 is spatially positioned directly in front of the end face of the multi-core optical fiber 20, and spaced a working distance from the end face of the multi-core optical fiber 20 along the Z-axis of the global coordinate system, to receive the initial beam from the transmitting optical fiber 27. During the measurement process, the optical modulation target 30 is rigidly fixed to the surface of the object under test via a base, thereby ensuring that it maintains a synchronous motion state with the object under test. Therefore, the microscale six-degree-of-freedom motion measurement device can accurately characterize the spatial motion trajectory and attitude changes of the object under test by measuring the six-degree-of-freedom pose change of the optical modulation target 30 relative to the multi-core optical fiber 20 in real time.

[0038] Furthermore, the reflected light spot formed by the backlight beam emitted by the transmitting fiber 27 and reflected by the four planar reflecting units of the optical modulation target 30, due to the change in the pose of the optical modulation target 30, forms a specific reflected light intensity distribution on the end face of the multi-core fiber 20 that dynamically changes with the pose; the six receiving fibers located on the common probe end face of the multi-core fiber 20 spatially sample the reflected light spot in their respective fiber core aperture areas, capturing a portion of the light energy of the reflected light intensity distribution.

[0039] Furthermore, the multi-channel photodetector 40 is located at the end of the multi-core optical fiber 20, that is, the receiving fiber probe in the separate connection end of the multi-core optical fiber 20 is connected one-to-one with the six independent photoelectric sensing channels of the multi-channel photodetector 40; the six photoelectric sensing channels of the multi-channel photodetector 40 are its input terminals. The multi-channel photodetector 40 is configured as a photoelectric conversion module, and its core function is to convert the six independent optical power signals transmitted from the receiving optical fiber in real time and synchronously. to These signals are converted into six corresponding analog electrical signals, and the amplitude of these six analog electrical signals represents the real-time light intensity received by the six receiving optical fibers.

[0040] Furthermore, the input terminal of the data acquisition card 50 is connected to the output terminal of the multi-channel photodetector 40, and it is configured as a signal acquisition and conversion module to receive the six analog electrical signals output by the multi-channel photodetector 40 and convert them into digital signals.

[0041] Furthermore, the processor 60 is communicatively connected to the data acquisition card 50 and is configured as the core of the entire device for computation and control. The processor 60 receives digital signals from the data acquisition card 50 and processes the signals using a preset light intensity distribution model and pose calculation algorithm, thereby calculating the six-degree-of-freedom pose parameters of the optical modulation target 30 relative to the multi-core optical fiber 20 in real time.

[0042] A method for measuring the six degrees of freedom (DOF) of microscale motion in a multi-core fiber optic cable based on a light intensity distribution model is proposed, implemented using the aforementioned multi-core fiber optic six-DOF motion measurement device. The multi-core fiber optic six-DOF motion measurement aims to measure the optical power of the six channels obtained from the actual measurements by the multi-channel photodetector 40. to The six-degree-of-freedom pose parameters of the optical modulation target 30 relative to the global coordinate system of the common probe end face of the multi-core optical fiber 20 are solved by reverse engineering. ,in, This represents the lateral translation of the optically modulated target 30 along the X-axis of the global coordinate system. This represents the lateral translation of the optically modulated target 30 along the Y-axis of the global coordinate system. This represents the lateral translation of the optically modulated target 30 along the Z-axis of the global coordinate system. This represents the pitch angle of the optically modulated target 30 as it rotates around the X-axis of the global coordinate system. This represents the pitch angle of the optically modulated target 30 as it rotates around the Y-axis of the global coordinate system. This represents the pitch angle of the optically modulated target 30 rotating around the Z-axis of the global coordinate system. To achieve this reverse solution, this invention establishes a unified forward mathematical model based on geometric optics and the light intensity distribution characteristics of a preset light source; the computational flow of this forward mathematical model covers the following core steps: First, based on the input pose parameters of the optically modulated target 30... The homogeneous coordinate transformation matrix is ​​used to solve the normal vector and spatial equation of each planar reflector in the global coordinate system in real time. Then, based on the principle of geometric optics reflection imaging, the virtual image point coordinates of the light source with respect to each planar reflector are derived, and the effective illumination area of ​​the reflected beam on the end face of the multi-core fiber 20 common probe is defined accordingly. The virtual image point coordinates are substituted into the preset Gaussian beam intensity distribution equation to construct the instantaneous radiation intensity distribution model of any sampling point on the end face of the multi-core fiber 20 common probe. Finally, by performing a double integral on the light intensity distribution at the geometric intersection of the effective illumination area and the core aperture area of ​​each receiving fiber, the theoretically required coupled optical power value to be captured by the six receiving fibers is calculated. to In a preferred embodiment of the present invention, in order to verify the effectiveness of the above mathematical model, the following system parameters are set: the light source is selected with a center wavelength. The red laser source has a beam waist radius set at the exit of the transmitting fiber optic cable. Central light intensity Normalized to 1, its preset light intensity distribution function adopts a Gaussian beam model. The light modulation target 30 adopts a four-sided hollow pyramidal prism structure, composed of four planar reflective units. These four planar reflective units converge at the origin of the target coordinate system. To achieve sensitive response to six degrees of freedom motion, the mirror surface of each planar reflective unit forms a preset fixed tilt angle with the plane of the target coordinate system. Specifically, it includes the following steps: The first step is to determine the known pose parameters of the optically modulated target 30. The target coordinate system is obtained by processing the data using the principle of homogeneous coordinate transformation. In the global coordinate system The homogeneous matrix of attitude and position in the target coordinate system is obtained; the homogeneous matrix is ​​then processed with the normal vectors of any point and each planar reflection unit in the target coordinate system using a homogeneous coordinate transformation method to obtain the global coordinate system. The normal vectors of any point and each planar reflection unit in the global coordinate system; By analyzing the normal vectors and common convergence vertices of each planar reflection element, the deterministic equations for each planar reflection element under the current pose are determined. Specifically: Step 1.1: Based on the known six-degree-of-freedom pose parameters of the optical modulation target 30 relative to the global coordinate system of the common probe end face of the multi-core optical fiber 20... ,in, This represents the lateral translation of the optically modulated target 30 along the X-axis of the global coordinate system. This represents the lateral translation of the optically modulated target 30 along the Y-axis of the global coordinate system. This represents the lateral translation of the optically modulated target 30 along the Z-axis of the global coordinate system. This represents the pitch angle of the optically modulated target 30 as it rotates around the X-axis of the global coordinate system. This represents the pitch angle of the optically modulated target 30 as it rotates around the Y-axis of the global coordinate system. This represents the pitch angle of the optically modulated target 30 rotating around the Z-axis of the global coordinate system; the six-degree-of-freedom pose parameters are processed using the homogeneous coordinate transformation principle, i.e., a homogeneous matrix is ​​introduced. Describe the target coordinate system In the global coordinate system The posture and position in the middle: (1) in, The relative pose of the optically modulated target 30 with respect to the common probe end face of the multi-core optical fiber 20, i.e., the input target coordinate system. In the global coordinate system The pose parameters are as follows; A homogeneous matrix representing the attitude and position of the target coordinate system in the global coordinate system.

[0043] Step 1.2 describes the transformation of any point and normal vector in the target coordinate system into the global coordinate system. This is done using the homogeneous matrix obtained in Step 1.1. The transformation of the homogeneous coordinates of any point in the target coordinate system and the mirror normal vector to the global coordinate system can be further described as follows: (2) in, and These represent the representations of any point in space in the global coordinate system and the target coordinate system, respectively. and These represent the normal vectors of each mirror surface of the optically modulated target 30 in the global coordinate system and the target coordinate system, respectively.

[0044] Assuming that the four planar reflective elements of the optically modulated target 30 are all ideal planes, and that they intersect at a point in the global coordinate system. Each planar reflecting unit can be described by the following deterministic equation: (3) in, The third of the optical modulation target 30 One planar reflective unit, of which The range is 1 to 4; Indicates the first The projection components of the normal vectors of each plane onto the X-axis of the global coordinate system. This represents the projection component on the Y-axis. Represents the projection components on the Z-axis, and the combination of the three is the first. Normal vectors of the planes , ; This represents the coordinate value of any point on the plane on the X-axis of the global coordinate system. This represents the coordinate value on the Y-axis. This represents the coordinate value on the Z-axis; the combination of the three values ​​is the first... An interior point on a plane , ; This represents the lateral translation of the optically modulated target 30 along the X-axis of the global coordinate system. This represents the lateral translation of the optically modulated target 30 along the Y-axis of the global coordinate system. This represents the lateral translation of the optical modulation target 30 along the Z-axis of the global coordinate system; the combination of these three factors constitutes the common convergence vertex of all the planar reflective units. O ,Right now In this embodiment, the four planar reflective units of the optical modulation target 30 are set to a preset fixed tilt angle of 10° relative to the XY plane of the target coordinate system. The first planar reflective unit in the target coordinate system... The initial normal vector in the target coordinate system is expressed as: Assuming the object under test causes the light-modulated target 30 to undergo a complex micro-motion involving translation and rotation, the input six-DOF pose parameters are set as follows: , , , , , The processor 60 calculates the homogeneous transformation matrix based on the above pose. : The first planar reflection unit in the target coordinate system The initial normal vector in the global coordinate system is represented as : First planar reflection unit The deterministic equations of the global coordinate system under this specific pose are solved as follows: The second step involves processing the spatial sampling points on the end face of the multi-core fiber 20 common probe and the deterministic equations of each planar reflection unit determined in the first step using a virtual image point mapping model to calculate the virtual image point coordinates of the sampling points with respect to each planar reflection unit. The geometric corner points and virtual image point coordinates of the light modulation target 30 are then processed using ray tracing and geometric projection methods to determine the effective illumination area of ​​the reflected beam on the end face of the multi-core fiber 20 common probe. First, a virtual image point mapping model is constructed to solve for the spatial midpoint. Relative to each planar reflection unit virtual image points Subsequently, all geometric corner points of the optical modulation target 30 are processed using a virtual image point mapping model to obtain all projected boundary points on the end face of the multi-core fiber 20; the topological boundaries of all projected boundary points are connected and the region is closed, finally defining and obtaining the effective illumination area corresponding to the reflected beam on the end face of the multi-core fiber 20. Specifically: Step 2.1: Construct a virtual image point mapping model to solve for the midpoint in space. Relative to each planar reflection unit virtual image points Specifically: vector ,and In the normal vector Projection on Described as: (4) therefore, Q Point on a plane Projection on Represented as: (5) and Q Virtual image of a point Based on the virtual pixel mapping model, the following formula can be derived: (6) The virtual image point Calculated using the following formula: (7) (8) (9) in, , , These respectively represent the calculated virtual image points. Coordinate components on the X, Y, and Z axes of the global coordinate system. , , These represent the coordinate components of any point in space whose image is to be obtained, located on the X, Y, and Z axes of the global coordinate system, respectively. , , and , , The meaning is the same as the definition in the aforementioned plane equation.

[0045] Step 2.2: Repeat the virtual image point mapping model described in Step 2.1 for all peripheral geometric corner points of the optical modulation target 30 to obtain all projected boundary points on the end face of the multi-core fiber 20. Perform topological boundary connection and region closure processing on all projected boundary points to finally define and obtain the effective illumination area corresponding to the reflected beam on the end face of the multi-core fiber 20. Specifically: The geometric features of the optically modulated target 30 are defined as key corner points in the global coordinate system: the Mth geometric corner point and the central convergence point are represented in the target coordinate system as follows: as well as Its coordinate transformation in the target coordinate system using a homogeneous matrix results in its representation in the global coordinate system. and a central convergence point To determine the above geometric corner points The corresponding projection boundary point on the end face of the multi-core fiber 20 common probe. The virtual image point mapping model established in step 2.1 is used for joint solution, specifically: First, calculate the light source point. L Passing through geometric corners The ray and the multi-core fiber 20 common probe end face reflect each other about the plane of the geometric corner point M. The virtual intersection point of the virtual mirror plane. According to geometric relationships, this virtual intersection point lies on the ray. Above, satisfying the ray equation: (10) in: , , These represent the geometric corners through which the light source point passes. The virtual intersection point of the ray and the virtual mirror plane of the reflection unit of the multi-core fiber 20 common probe end face about the geometric corner point M. Coordinate components on the X, Y, and Z axes of the global coordinate system; Represents the geometric corners of the optically modulated target. Coordinate vector in the global coordinate system; Represents the scaling parameters of the ray equation; This indicates the direction from the light source point L to the geometric corner point. The direction vector.

[0046] At the same time, this virtual intersection Z-axis component Determined by the geometric intercept of each planar reflection unit, the result is obtained using a virtual image point mapping model: (11) Solve the parameters simultaneously Then, determine the virtual intersection point. Complete coordinates, then Derived from the following formula: (12) (13) in: , Representing geometric corner points After the first After reflection by each planar reflector unit, the projected boundary point on the end face of the 20-core fiber common probe is... Coordinate components on the X and Y axes of the global coordinate system; This represents the projection component of the plane's normal vector onto the X-axis of the global coordinate system. This represents the projection component on the Y-axis. Represents the projection components on the Z-axis, and the combination of the three is the first. Normal vectors of the planes , ; , , The meaning is the same as the previous definition, representing the coordinate components of the common converging vertices.

[0047] Repeat the above calculations for all geometric corner points to obtain the four projected vertices on the end face of the multi-core fiber 20 common probe. to Based on the topological connections of these vertices, the effective illumination area corresponding to each planar reflective unit on the end face of the multi-core fiber 20 common probe is obtained. The core of this step lies in establishing a mathematical mapping of the reflection process through geometric transformation. The virtual image point refers to the virtual source point emitted from symmetrical positions behind each planar reflection unit of the light modulation target 30, based on the plane reflection law; the effective illumination area refers to the actual spot coverage area projected onto the common probe end face of the multi-core optical fiber 20 after being modulated and reflected by the light modulation target 30.

[0048] The third step, based on the effective lighting area determined in the second step, involves the processor 60 calculating the sampling point on the end face of the multi-core fiber optic 20 common probe. The light intensity distribution function at the location. Specifically, a schematic diagram of the geometric optical reflection imaging principle based on virtual image points in this embodiment of the invention is shown below. Figure 6 As shown, according to the principle of geometrical optics reflection imaging, the sampling point located on the end face of the multi-core fiber 20 receives the image after passing through the first... The intensity of light reflected from a plane is physically equivalent to the intensity of the initial beam of light that, without reflection, propagated directly to that point with respect to the plane. The light intensity at the virtual image point. Specifically: First, processor 60, based on the virtual image point mapping model constructed in step 2.1, maps the sampling points on the common probe end face of multi-core fiber 20. Substituting the global coordinates, the coordinate components of the corresponding virtual image point in the global coordinate system are calculated as follows: (14) (15) (16) in: The third of the optical modulation target 30 There are planes, among which The range is 1 to 4; The calculated coordinate components of the virtual image point on the X-axis of the global coordinate system represent the coordinate components of the virtual image point. Represents the coordinate components on the Y-axis. The three components, representing the coordinates on the Z-axis, are combined to form the virtual image point. ; This represents the projection component of the plane's normal vector onto the X-axis of the global coordinate system. This represents the projection component on the Y-axis. Represents the projection components on the Z-axis, and the combination of the three is the first. Normal vectors of the planes ; This represents the coordinates of the convergent vertex of all planar reflection units on the X-axis of the global coordinate system. This represents the coordinate value on the Y-axis. These represent the coordinate values ​​on the Z-axis; the combination of these three values ​​constitutes the common converging vertex. O ,Right now ; This indicates a sampling point on the end face of the multi-core fiber optic 20 common probe. Projection components on the X-axis of the global coordinate system This represents the coordinate value on the Y-axis. The point lies in the XY plane of the global coordinate system, therefore the combination of the two forms the... .

[0049] Processor 60 will virtual pixel Substituting into the Gaussian beam intensity distribution equation, calculate the virtual image point. Light intensity distribution function : (17) in, For virtual image points The radiation intensity at that location, The intensity is the central light intensity at the waist of the beam, which is the maximum intensity at the start of the beam propagation. The waist radius is the radius of the beam at its narrowest point. The distance between the waist and the Z-axis direction The beam radius at that location is calculated using the following formula: ,in The Rayleigh length is calculated using the following formula: , Given the laser wavelength of 660 nm, the Rayleigh length can be calculated. . , , For virtual image points The X, Y, and Z coordinate components in the global coordinate system. Similarly, when using other light beams, simply replace the corresponding intensity distribution function.

[0050] The fourth step involves integrating and superimposing the received fiber-coupled optical power. This is based on the solution obtained in the third step regarding the virtual image points. The light intensity distribution function is calculated, and the processor 60, combined with the physical structure parameters of the multi-core optical fiber 20, performs numerical integration to solve for the actual optical power captured by the N receiving optical fibers. Specifically: The acquisition of 40 pairs of optical signals by a multi-channel photodetector is mathematically equivalent to integrating the light intensity within the effective aperture of the receiving fiber core. The domain of the integration interval depends on the intersection of the effective illumination region and the effective aperture region of the receiving fiber. One planar reflective unit Reflected and by the first The optical power captured by a receiving optical fiber is defined as optical intensity. The double integral over the intersection of the effective illumination area and the receiving fiber core area is calculated using the following formula: (18) Since the optical modulation target 30 contains four planar reflective units, the first The total optical power output by the receiving fiber is the linear superposition of the component optical powers contributed by the four planar reflecting units. The specific calculation formula is as follows: (19) (20) in, Indicates the first The root receiving fiber from the first The component light power received by each planar reflector unit; Indicates by the first The effective lighting area generated by each planar reflective unit; Indicates the first The core aperture region of the receiving optical fiber; This represents the geometric intersection of two regions; , , Coordinates of the end face of the 20-core fiber common probe Corresponding virtual image points The coordinate components in the global coordinate system have values ​​that vary with the integration position. Change with change; Indicates the first The total theoretical optical power output from the receiving fiber is the final output of the forward mathematical model. This value is used to compare the residuals of the signals actually acquired by the multi-channel photodetector 40, thereby achieving inverse pose optimization. Since analytical integration is difficult to solve directly, the processor 60 uses a discretized numerical integration method to calculate the core aperture region from the first receiving fiber 21 to the sixth receiving fiber 26. The grid is divided into micro-element meshes. For each pose, the processor traverses the mesh points 60 times and accumulates the light intensity values.

[0051] The above embodiments are merely illustrative of the implementation methods of the present invention, but should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the protection scope of the present invention.

Claims

1. A microscale six-degree-of-freedom motion measurement device based on a light intensity distribution model, characterized in that, The microscale six-degree-of-freedom motion measurement device includes a laser diode and laser coupler (10), a multi-core optical fiber (20), an optically modulated target (30), a multi-channel photodetector (40), a data acquisition card (50), and a processor (60); The laser diode and laser coupler (10) form a light source system, which is connected to the transmitting fiber (27) in the multi-core fiber (20) through a fiber optic connector; The multi-core fiber (20) is used for beam transmission and spatial sampling. Its probe end face adopts a central emission and surrounding reception arrangement. The central emission fiber (27) is used to project the beam of the laser diode and laser coupler (10) onto the optical modulation target (30). N receiving fibers connected to the multi-channel photodetector (40) are evenly distributed around the emission fiber (27). The optical modulation target (30) is arranged in front of the probe end face of the multi-core fiber (20). When the optical modulation target (30) undergoes a six-degree-of-freedom pose change with the object under test, its multi-faceted pyramidal reflection structure, composed of multiple planar reflection units that are circumferentially distributed around the central axis and have a common convergence vertex and a preset tilt angle, modulates the received initial beam and reflects the light spot back to the probe end face of the multi-core fiber (20) to form a specific light intensity distribution that dynamically changes with the pose. The multi-channel photodetector (40) synchronously converts the N optical power signals into analog electrical signals, which are then converted from analog to digital by the data acquisition card (50) and uploaded to the processor (60). The processor (60) outputs the six-degree-of-freedom pose parameters of the optical modulation target (30) relative to the multi-core optical fiber (20).

2. The microscale six-degree-of-freedom motion measurement device based on a light intensity distribution model according to claim 1, characterized in that, In the microscale six-degree-of-freedom motion measurement device: The multi-core optical fiber (20) consists of a common probe end and discrete connection ends; the end face of the receiving optical fiber is flush with the probe end face of the multi-core optical fiber (20), and the captured N independent optical power signals are transmitted to the multi-channel photodetector (40) through the multi-core optical fiber (20). The laser diode and laser coupler (10) consists of two parts: a laser diode and a laser coupler. The laser diode is used to generate the initial beam, and the initial beam is transmitted to the transmitting fiber (27) through the laser coupler. In the multi-core optical fiber (20), a transmitting optical fiber (27) and at least one receiving optical fiber are encapsulated and integrated, that is, the number of receiving optical fibers N≥1; the transmitting optical fiber (27) is located at the center of the multi-core optical fiber (20); the receiving optical fiber is located around the transmitting optical fiber (27), and each receiving optical fiber constitutes an independent light intensity extraction channel. By capturing the light intensity of the reflected light field at different spatial positions, the six-degree-of-freedom pose change of the object under test is converted into a multi-parallel optical power signal. The light modulation target (30) is a reflective component with a preset spatial geometry structure, which encodes its six-degree-of-freedom pose change as a change in the reflected light intensity distribution. Specifically, the light modulation target (30) contains K planar reflective units distributed circumferentially around the central axis. The K planar reflective units have a common geometric convergence vertex in space, and the mirror normal vector of each planar reflective unit is at a preset non-zero tilt angle with the central axis of the light modulation target (30).

3. The microscale six-degree-of-freedom motion measurement device based on a light intensity distribution model according to claim 2, characterized in that, The optical modulation target (30) includes K geometric corner points, which are located at the outer geometric vertices of the front-end planar reflective unit of the optical modulation target (30), and together define the outer contour boundary of the effective reflection area of ​​the optical modulation target (30); the optical modulation target (30) as a whole forms a K-faceted angular pyramidal mirror structure with a central concave or convex shape; when the incident beam irradiates the optical modulation target (30), different planar reflective units divide the beam and reflect it to different spatial regions; when the optical modulation target (30) undergoes translation or rotation, the energy distribution of the light spot on the common probe end face of the multi-core fiber (20) will undergo a specific nonlinear change due to the geometric projection change of each planar reflective unit; During the measurement process, the optical modulation target (30) is fixed to the surface of the object to be measured. By measuring the six degrees of freedom pose change of the optical modulation target (30) relative to the multi-core optical fiber (20) in real time, the spatial motion trajectory and attitude change of the object to be measured can be accurately characterized.

4. The microscale six-degree-of-freedom motion measurement device based on the light intensity distribution model according to claim 3, characterized in that, If there are two or more receiving optical fibers, i.e. N≥2, they are evenly distributed around the transmitting optical fiber (27), and a discrete spatial sampling array is constructed on the end face of the multi-core optical fiber (20).

5. A microscale six-degree-of-freedom motion measurement method based on a light intensity distribution model, characterized in that, The microscale six-degree-of-freedom motion measurement device based on the light intensity distribution model described in any one of claims 1-4 is implemented; a positive mathematical model is established, and its calculation process is as follows: First, according to the input light modulation target (30) pose parameters, the normal vector and spatial equation of each planar reflection unit in the global coordinate system are solved in real time using the homogeneous coordinate transformation matrix; Subsequently, based on the principle of geometric optical reflection imaging, the virtual image point coordinates of the light source with respect to each planar reflection unit are derived, and the effective illumination area of ​​the reflected beam on the end face of the common probe of the multi-core fiber (20) is defined accordingly. The virtual image point coordinates are substituted into the preset Gaussian beam intensity distribution equation to construct the instantaneous radiation intensity distribution model of any sampling point on the end face of the common probe of the multi-core fiber (20). Finally, by performing a double integral on the light intensity distribution at the geometric intersection of the effective illumination area and the core aperture area of ​​each receiving fiber, the theoretically required coupled optical power value to be captured by the N receiving fibers is calculated. to ; Specifically, the following steps are included: The first step is to process the known pose parameters of the optically modulated target (30) using homogeneous coordinate transformation to obtain the target coordinate system. In the global coordinate system The homogeneous matrices of the pose and position in the target coordinate system are obtained; the homogeneous coordinate transformation method is used to process the homogeneous matrices with any point in the target coordinate system and the mirror normal vector to obtain the global coordinate system. Given any point in the coordinate system and the normal vectors of each mirror; based on the global coordinate system... The normal vectors of each mirror surface and their common converging vertex are used to determine the deterministic equations of each planar reflection unit under the current pose. The second step involves processing the spatial sampling points on the end face of the multi-core fiber (20) common probe and the deterministic equations of each planar reflection unit determined in the first step using a virtual image point mapping model to calculate the virtual image point coordinates of the sampling points with respect to each planar reflection unit; the geometric corner points and virtual image point coordinates of the light modulation target (30) are processed using ray tracing and geometric projection methods to determine the effective illumination area of ​​the reflected beam on the end face of the multi-core fiber (20) common probe. In the third step, based on the effective illumination area determined in the second step, the processor (60) calculates the light intensity distribution function at the sampling points on the common probe end face of the multi-core fiber (20). According to the principle of geometric optical reflection imaging, the light intensity received by the sampling points located on the end face of the multi-core fiber (20) after passing through the first... The light intensity reflected by each planar reflector unit is equivalent to the initial beam propagating directly to the sampling point without reflection, with respect to the plane. The light intensity at the virtual image point is obtained, which gives the light intensity distribution function for the virtual image point; The fourth step is to solve for the integration and superposition of the received fiber-coupled optical power; Based on the light intensity distribution function of the virtual image point obtained in the third step, the processor (60) combines the physical structure parameters of the multi-core optical fiber (20) to numerically integrate and solve the actual light power captured by the N receiving optical fibers.

6. The microscale six-degree-of-freedom motion measurement method based on a light intensity distribution model according to claim 5, characterized in that, The first step is specifically as follows: Establish a global coordinate system using the right-hand coordinate system rule. The origin O of the global coordinate system is located at the center of the probe end face of the multi-core fiber (20). The Z-axis coincides with the core axis of the transmitting fiber (27), and its positive direction is defined as the emission direction of the light, that is, the direction perpendicular from the end face of the transmitting fiber (27) to the optical modulation target (30). The Y-axis is located on the end face of the transmitting fiber (27), and its positive direction is defined as the direction from the origin O to the core center of the multi-core fiber (20). The X-axis is determined by the right-hand coordinate system rule. At the same time, in order to accurately describe the six degrees of freedom motion of the optical modulation target (30) relative to the multi-core fiber (20), a target coordinate system fixed to the optical modulation target (30) is established. The origin O' is defined as the common geometric convergence vertex of each planar reflection unit of the optical modulation target (30). A zero pose state is defined: in this zero pose state, the optical modulation target (30) does not rotate and its origin O' is located on the Z-axis of the global coordinate system. The Z' axis is defined as the principal axis of the target coordinate system. In the zero pose state, the Z' axis is parallel and in the same direction as the Z-axis of the global coordinate system. The Y' axis is defined as parallel and in the same direction as the Y-axis of the global coordinate system in the zero pose state. The X' axis is determined according to the right-hand coordinate system rule. In the zero pose state, the X' axis is parallel and in the same direction as the X-axis of the global coordinate system. Step 1.1: Based on the known six-degree-of-freedom pose parameters of the optical modulation target (30) relative to the global coordinate system of the common probe end face of the multi-core optical fiber (20), ,in, This represents the lateral translation of the optically modulated target (30) along the X-axis of the global coordinate system. This represents the lateral translation of the optically modulated target (30) along the Y-axis of the global coordinate system. This represents the lateral translation of the optically modulated target (30) along the Z-axis of the global coordinate system. The pitch angle represents the rotation of the optically modulated target (30) around the X-axis of the global coordinate system. The pitch angle represents the rotation of the optically modulated target (30) around the Y-axis of the global coordinate system. The pitch angle of the optically modulated target (30) rotating around the Z-axis of the global coordinate system is represented; the six-degree-of-freedom pose parameters are processed using the homogeneous coordinate transformation principle, that is, a homogeneous matrix is ​​introduced. Describe the target coordinate system In the global coordinate system The posture and position in the middle: （1） in, The relative pose of the optically modulated target (30) with respect to the common probe end face of the multi-core optical fiber (20), i.e., the input target coordinate system. In the global coordinate system The pose parameters are as follows; A homogeneous matrix representing the attitude and position of the target coordinate system in the global coordinate system; Step 1.2 describes the transformation of any point and normal vector in the target coordinate system in the global coordinate system; using the homogeneous matrix obtained in Step 1.

1. The transformation of the homogeneous coordinates of any point in the target coordinate system and the mirror normal vector to the global coordinate system can be further described as follows: （2） in, and These represent the representations of any point in space in the global coordinate system and the target coordinate system, respectively. and These represent the normal vectors of each mirror surface of the optically modulated target (30) in the global coordinate system and the target coordinate system, respectively; Assuming that the K planar reflective units of the optically modulated target (30) are all ideal planes, intersecting at points in the global coordinate system. Each planar reflecting unit is described by the following deterministic equation: （3） in, The first part representing the optical modulation target (30) One planar reflective unit, of which The range is from 1 to K; Indicates the first The projection components of the normal vectors of each plane onto the X-axis of the global coordinate system. This represents the projection component on the Y-axis. Represents the projection components on the Z-axis, and the combination of the three is the first. Normal vectors of the planes , ; This represents the coordinate value of any point on the plane on the X-axis of the global coordinate system. This represents the coordinate value on the Y-axis. This represents the coordinate value on the Z-axis; the combination of the three values ​​is the first... An interior point on a plane , ; This represents the lateral translation of the optically modulated target (30) along the X-axis of the global coordinate system. This represents the lateral translation of the optically modulated target (30) along the Y-axis of the global coordinate system. This represents the lateral translation of the optically modulated target (30) along the Z-axis of the global coordinate system; the combination of these three elements forms the common convergence vertex of each planar reflective unit. O ,Right now .

7. The microscale six-degree-of-freedom motion measurement method based on a light intensity distribution model according to claim 6, characterized in that, The second step is as follows: Step 2.1: Construct a virtual image point mapping model to solve for the midpoint in space. Relative to each planar reflection unit virtual image points , Specifically: vector ,and In the normal vector Projection on Described as: （4） therefore, Q Point on a plane Projection on Represented as: （5） and Q Virtual image of a point Based on the virtual pixel mapping model, the following formula is derived: （6） Virtual pixels Calculated using the following formula: （7） （8） （9） in, , , They represent the calculated virtual image points respectively. Coordinate components on the X, Y, and Z axes of the global coordinate system; , , These represent the coordinate components of any point in space whose image is to be obtained, located on the X, Y, and Z axes of the global coordinate system, respectively. , , and , , The meaning is the same as the definition in the aforementioned plane equation; Step 2.2: Repeat step 2.1 to process all peripheral geometric corner points of the optical modulation target (30) to obtain all projected boundary points on the end face of the multi-core fiber (20). Perform topological boundary connection and region closure processing on all projected boundary points to finally define and obtain the effective illumination area corresponding to the reflected beam on the end face of the multi-core fiber (20); Specifically: The geometric features of the optically modulated target (30) are defined as the key corner points in the global coordinate system: the Mth geometric corner point and the central convergence point are represented in the target coordinate system as: as well as Its representation in the target coordinate system, after coordinate transformation using a homogeneous matrix, is then expressed in the global coordinate system. and a central convergence point To determine the above geometric corner points The corresponding projection boundary point on the end face of the common probe of the multi-core optical fiber (20) The virtual image point mapping model established in step 2.1 is used for joint solution, specifically: First, calculate the light source point. L Passing through geometric corners The common probe end face of the ray and multi-core optical fiber (20) reflects the plane of the geometric corner point M. The virtual intersection point of the virtual mirror plane; according to geometric relationships, this virtual intersection point lies on the ray. Above, satisfying the ray equation: （10） in: , , These represent the geometric corners through which the light source point passes. The virtual intersection of the ray and the virtual mirror plane of the reflection unit of the multi-core fiber (20) common probe end face about the geometric corner point M. Coordinate components on the X, Y, and Z axes of the global coordinate system; Represents the geometric corners of the optically modulated target. Coordinate vector in the global coordinate system; Represents the scaling parameters of the ray equation; This indicates the direction from the light source point L to the geometric corner point. The direction vector; Meanwhile, virtual intersection Z-axis component Determined by the geometric intercept of each planar reflection unit, the result is obtained using a virtual image point mapping model: （11） Solve the parameters simultaneously Then, determine the virtual intersection point. Complete coordinates, then Derived from the following formula: （12） （13） in: , Representing geometric corner points After the first After reflection by each planar reflector unit, the projected boundary point on the end face of the common probe of the multi-core optical fiber (20) is... Coordinate components on the X and Y axes of the global coordinate system; This represents the projection component of the plane's normal vector onto the X-axis of the global coordinate system. This represents the projection component on the Y-axis. Represents the projection components on the Z-axis, and the combination of the three is the first. Normal vectors of the planes , ; Calculations were performed on all geometric corner points to obtain K projected vertices on the end face of the common probe of the multi-core fiber (20). to This allows us to obtain the effective illumination area corresponding to each planar reflective unit on the end face of the common probe of the multi-core fiber (20). .

8. The microscale six-degree-of-freedom motion measurement method based on the light intensity distribution model according to claim 7, characterized in that, The third step specifically involves: First, the processor (60) uses the virtual image point mapping model constructed in step 2.1 to sample the points on the common probe end face of the multi-core fiber (20). Substitute the global coordinates to calculate the coordinate components of the corresponding virtual image point in the global coordinate system; （14） （15） （16） in: The first part representing the optical modulation target (30) There are planes, among which The range is from 1 to K; This represents the coordinate components of the virtual image point on the X-axis of the global coordinate system. Represents the coordinate components on the Y-axis. The three components, representing coordinates on the Z-axis, are combined to form a virtual image point. ; This represents the projection component of the plane's normal vector onto the X-axis of the global coordinate system. This represents the projection component on the Y-axis. Represents the projection components on the Z-axis, and the combination of the three is the first. Normal vectors of the planes ; This represents the coordinates of the convergent vertex of all planar reflection units on the X-axis of the global coordinate system. This represents the coordinate value on the Y-axis. This represents the coordinate value on the Z-axis; the combination of these three values ​​forms the common converging vertex. O ,Right now ; This indicates a sampling point on the end face of the common probe of the multi-core optical fiber (20). Projection components on the X-axis of the global coordinate system This represents the coordinate value on the Y-axis. The point lies in the XY plane of the global coordinate system, therefore the two are combined as follows: ; The processor (60) will virtual image points Substituting into the Gaussian beam intensity distribution equation, calculate the virtual image point. Light intensity distribution function : （17） in, For virtual image points The radiation intensity at that location, The light intensity at the center of the waist section; The waist radius; The distance between the waist and the Z-axis direction The beam radius at that location; , , For virtual image points The X, Y, and Z coordinate components in the global coordinate system.

9. The microscale six-degree-of-freedom motion measurement method based on a light intensity distribution model according to claim 8, characterized in that, In the third step, The calculation formula is: ,in The Rayleigh length is calculated using the following formula: , is the laser wavelength.

10. The microscale six-degree-of-freedom motion measurement method based on a light intensity distribution model according to claim 9, characterized in that, The fourth step is specifically as follows: By the One planar reflective unit Reflected and by the first The optical power captured by a receiving optical fiber is defined as optical intensity. The double integral over the intersection of the effective illumination area and the receiving fiber core area is calculated using the following formula: (18) Since the optically modulated target (30) contains K planar reflective units, the first The total optical power output by the receiving optical fiber is the linear superposition of the component optical powers contributed by the K planar reflecting units. The specific calculation formula is as follows: (19) (20) in, Indicates the first The root receiving fiber from the first The component light power received by each planar reflector unit; Indicates by the first The effective lighting area generated by each planar reflective unit; Indicates the first The core aperture region of the receiving optical fiber; This represents the geometric intersection of two regions; , , Coordinates of the common probe end face of the multi-core fiber (20) Corresponding virtual image points Coordinate components in the global coordinate system; Indicates the first The total theoretical optical power output from the root receiving fiber is the final output, which is used to compare the residuals of the signals actually collected by the multi-channel photodetector (40) to achieve reverse pose optimization solution.

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