Method for measuring three-dimensional surface topography of a mirror based on projected moire

Abstract

A kind of mirror three-dimensional topography measurement method based on projection moire, by setting the surface light source for displaying stripe at the incident end of the plane to be measured, setting the optical equipment, reference grid and image acquisition device at the exit end, according to the moire pattern formed by the reflection image of the plane to be measured and the reference grid, through mirror projection moire model, three-dimensional topography is obtained by mirror moire topography solving.The height-gradient ambiguity problem existing in single-camera single-display system is solved by changing light source, measurement model, calibration process and topography solving method, and full-field three-dimensional topography high-resolution measurement of free mirror with resolution better than 1 microns can be realized.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of three-dimensional topography measurement, and particularly relates to a mirror three-dimensional topography measurement method based on projected cloud patterns. BACKGROUND

[0002] Existing mirror three-dimensional topography measurement technologies are mostly based on interference methods, and need complex and precise experimental equipment and harsh experimental environments, and most of them are only suitable for regular mirror surface / topography measurement, and cannot meet the requirements of batch full-field high-precision detection of free mirror topography in industrial production. SUMMARY

[0003] The present application is aimed at the deficiency that the existing adaptive projected cloud pattern technology for continuous surfaces is only suitable for surface diffuse reflection and the light intensity in each direction is nearly consistent, and cannot be applied to mirror surface topography measurement, and proposes a mirror three-dimensional topography measurement method based on projected cloud patterns, which changes the light source, measurement model, calibration process and topography solving method, solves the height-gradient ambiguity problem existing in the single-camera single-display system, and can realize high-resolution full-field three-dimensional topography measurement of free mirrors with a resolution better than 1 micrometer.

[0004] The present application is realized by the following technical scheme:

[0005] The present application relates to a mirror three-dimensional topography measurement method based on projected cloud patterns, which sets a surface light source for displaying stripes at the incident end of the measured plane, sets an optical device, a reference grating and an image acquisition device at the exit end, obtains the three-dimensional topography through a mirror projected cloud pattern model and mirror cloud pattern topography solving according to the cloud pattern formed by the reflection image of the measured plane and the reference grating.

[0006] The mirror projected cloud pattern model refers to a relationship model among the cloud pattern phase, the measured mirror height and the two-direction slopes, which is established by using the ray tracing method and based on the mirror reflection theorem, and specifically is: the coordinates of the measured point P and the point B on the display reflected by the measured point P in the cloud pattern receiving system optical center O composed of the exit end optical device, the reference grating and the image acquisition device are taken as the origin of the coordinate system, e and the relationship expression between the measured point slope and the measured point height is established by the mirror reflection law, wherein: the two-direction slopes of the measured point P are represented by the subscript, the superscript represents the object of the slope, and U and v are the pixel coordinates of point P in the reflection image, the equivalent image principal point coordinates of the cloud pattern receiving system are represented by the subscript, and the superscript represents the cloud pattern receiving system, The two-direction focal lengths of the moire receiving system, the subscript indicates the focal length direction, the superscript represents the moire receiving system, σ2, σ3, σ4 are the first-order term parameters of the height of the measured point P in the moire receiving system coordinate system σ1, σ5, σ6, σ7, σ8 are the combination parameters of the camera parameters and the moire phase.

[0007] The combination parameters can be obtained by calibration and actual measurement.

[0008] The combination parameters and the first-order term parameters are respectively:

[0009]

[0010]

[0011]

[0012]

[0013]

[0014]

[0015]

[0016]

[0017] Wherein: φ x , φ y are two-direction moire phases obtained by actual collection and solving, the subscript indicates different directions, is the initial value of the phase of the surface light source stripe, is the initial value of the phase of the reference grating, is the camera principal point coordinate in the image acquisition system, p1 is the period length of the surface light source stripe, p2 is the grating line distance (period length) of the reference grating, is the camera x, y direction focal length, the superscript represents the camera, is the rotation matrix and translation matrix from the grating coordinate system to the camera coordinate system, which are 3*3 and 3*1 matrices respectively, are the rotation matrix and translation matrix from the virtual image coordinate system of the surface light source to the equivalent camera coordinate system, which are 3*3 and 3*1 matrices respectively.

[0018] The mirror moire topography solving specifically includes:

[0019] Step 1) The relationship between the adjacent measured point height and the slope is introduced by using the topography continuity assumption, that is, the Southwell model, which is specifically: Wherein: and are the coordinates and slope of the i-th row and j-th column measured point in the region of interest, and M and N are the number of rows and columns of the measured points in the region of interest.

[0020] Step 2) using the moire data at two positions, the height of any measured point is determined The optimization variable is to minimize the distance, specifically: Wherein: And are the three-dimensional point cloud coordinate data obtained by the two-position surface light source display after assuming the same height of the measured point.

[0021] Step 3) when the distance is minimized, the point cloud composed of the measured point coordinates obtained at any surface light source position is the final measured three-dimensional topography data of the measured mirror surface.

[0022] The present application relates to a kind of system for realizing the above-mentioned method, including: stripe projection unit, moire receiving system unit and data processing unit, wherein: stripe projection unit is according to the stripe image information sent by computer, display specified stripe pattern on display, and realize the switching of stripe pattern in measurement process;Moire receiving system unit receives mirror surface stripe information after, forms moire on reference grid occurs geometric interference, and the formed moire pattern is collected by camera;Data processing unit obtains the moire pattern information according to, according to the mirror projection moire model and mirror moire topography solving method proposed, calculates the three-dimensional topography result of measured mirror. BRIEF DESCRIPTION OF DRAWINGS

[0023] Figure 1 It is the structural schematic diagram of the present application;

[0024] In the figure: display 1, measured mirror surface 2, imaging lens 3, displacement platform and grating 4, shell 5, camera 6, control module 7;

[0025] Figure 2 It is the schematic diagram of mirror projection moire model;

[0026] Figure 3 It is the example implementation scene explanatory drawing;

[0027] In the figure: (a) is the overall schematic diagram of example system, (b) is the internal schematic diagram of moire receiving system used in example;

[0028] Figure 4 It is the flow chart of the present application;

[0029] Figure 5 It is the relevant image and data of measuring concave mirror;

[0030] In the figure: (a) is the original image, (b) is the cloud pattern after removing high-frequency noise, (c) is the cloud pattern wrapped phase distribution, (d) is the cloud absolute phase distribution;

[0031] Figure 6 The measured result is a concave mirror;

[0032] In the figure: (a) is the measured three-dimensional topography of the concave mirror, (b) is the residual distribution of the measured result, (c) is the comparison curve of the lowest profile line of the measured result and the standard value and the existing method. DETAILED DESCRIPTION

[0033] As shown in Figure 1 , Figure 2 and Figure 3 , the embodiment relates to a projection cloud pattern system for a continuous mirror, comprising a display 1 as a surface light source, a mirror to be measured 2, a receiving system comprising an imaging lens 3, a grating 4, a shell 5, a camera 6, and a control module 7 for sending and receiving signals, wherein: the control module 7 sends the required stripe image information to the display 1, sends the signal of moving the grating to the displacement platform in the grating 4 and the displacement platform, and receives the cloud pattern image information recorded by the camera 6, and finally calculates the three-dimensional topography of the mirror to be measured 2 by image processing.

[0034] In the embodiment, the resolution of the display is 2388*1668, which is used for projecting the stripe pattern.

[0035] In the embodiment, the imaging lens 3 adopts but is not limited to a zoom long-focus lens, which is used for receiving the stripe pattern reflected by the mirror and converging on the grating. The imaging lens 3 is fixed on the shell 5 through a special bayonet.

[0036] The displacement platform and the grating 4 comprise a piezoelectric ceramic displacement platform and a machine-etched grating. The piezoelectric ceramic displacement platform is a two-dimensional displacement platform, which can realize the movement of the grating with a positioning accuracy of 3 nm in two directions in the plane; the machine-etched grating selects a suitable grating pitch and area according to the actual measurement requirement, and the function is to form a cloud pattern by geometrically interfering with the mirror stripe pattern converged on the grating.

[0037] In the embodiment, the resolution of the camera 6 is 5472*3648, which is used for collecting the cloud pattern image.

[0038] The control module 7 is connected with the display 1, the camera 6 and the displacement platform controller respectively, realizes the display of the stripe image, the collection of the cloud pattern image and the control of the displacement platform, and realizes the processing of the collected cloud pattern image to calculate the three-dimensional topography data of the mirror to be measured 2.

[0039] As shown in Figure 4The embodiment is a projection grating-based mirror three-dimensional profile measurement method based on the above system, and specifically includes the following steps:

[0040] Step 1) Adjust the receiving system settings: adjust the focusing ring of the imaging lens, so that the focusing ring number is close to the distance between the receiving system and the measured mirror; adjust the focal length of the imaging lens, so that the target measured area occupies a suitable size of the camera image; adjust the camera lens focal length, so that the camera can clearly image the pattern of the measured mirror position.

[0041] Step 2) Calibrate the equivalent camera internal parameters and the reference mirror, and display the first position corresponding to the external parameters: use the display to display the checkerboard calibration board, change the position and attitude of the calibration board multiple times, and shoot the corresponding checkerboard pattern for calibrating the equivalent camera internal parameters; select a position near the measured mirror as the reference mirror position, place the calibration board at this position to shoot the checkerboard pattern, which is used to calibrate the equivalent camera external parameters corresponding to the reference mirror; select a suitable display measurement position, so that the stripe pattern of the display can be reflected by the measured mirror and then be shot by the receiving system; place the standard plane mirror at the determined reference mirror position, and place the display at the confirmed measurement position, and use the receiving system to shoot the checkerboard pattern of the virtual image of the display inside the reference mirror, which is used to calibrate the external parameters corresponding to the virtual image position of the display.

[0042] The equivalent camera, i.e. the cloud grating receiving system, can be regarded as a camera with inverted image during the calibration process.

[0043] Step 3) Shoot the cloud grating image under the first position of the display: according to the fineness of the stripes, select the grating with a frequency close to the reference grating in the image, adjust the position of the moving platform so that the grating is located at the focal plane position of the camera, and form a clear cloud grating pattern with the stripes; shoot four cloud grating patterns formed by each of the four stripe patterns with a phase difference of π / 4 and the four reference grating patterns with a phase difference of π / 4 under the measured mirror.

[0044] Step 4) Shoot the cloud grating image under the second position of the display: move the display position, so that the display stripe pattern received by the receiving system can still cover the measured mirror measurement area and form a clear cloud grating with the reference grating; shoot four cloud grating patterns formed by each of the four stripe patterns with a phase difference of π / 4 and the four reference grating patterns with a phase difference of π / 4 under the second position of the display.

[0045] The second position refers to any display position under the condition that the same display stripe in the image can still cover the measured mirror and form a clear cloud grating with the grating.

[0046] Step 5) calibrate the display second position corresponding to the external parameter, and receive the camera parameter in the system: replace the measured mirror with the reference mirror, the display displays the same checkerboard pattern as before, the receiving system takes the reference mirror under the calibration board checkerboard pattern, which is used to calibrate the equivalent camera external parameter corresponding to the display second position; replace the reference grid with the calibration board, take the checkerboard pattern at the reference grid position, which is used to calibrate the camera external parameter corresponding to the reference grid; change the pose of the calibration board, take multiple checkerboard patterns, which are used to calibrate the camera internal parameter.

[0047] The calibration is obtained by Zhang Zhengyou calibration method.

[0048] Step 6) using the mirror projection cloud pattern model and the mirror cloud pattern topography solving method, the cloud pattern phase is used to solve the three-dimensional topography of the mirror.

[0049] Through specific actual experiments, the projection cloud pattern method based on the above-mentioned system for continuous mirror, through the display 1 as a surface light source, the sinusoidal fringe is projected to the measured mirror surface, after the modulation reflection of the mirror, it enters the receiving system and interacts with the grating to form the cloud pattern, and is recorded by the camera 6. In order to facilitate the measurement of measurement error, the measured mirror adopts a concave mirror with a curvature radius of 51.20mm, the average absolute error (MAE) of the profile line calculated by the mirror projection cloud pattern method of the present application is 0.0019mm, and the MAE of the profile line calculated by the existing monocular single screen phase deflection method is 0.0073mm, and the specific experimental data is as shown in Figure 6 and Table 1.

[0050] Table 1 corresponds Figure 6 Data (part)

[0051]

[0052]

[0053] In summary, compared with the prior art, the present method constructs a mirror projection cloud pattern model and solves the mirror cloud pattern topography, and uses a display as a surface light source, so that the projection cloud pattern technology can be used for measuring the three-dimensional topography of the mirror; compared with other existing mirror three-dimensional topography measurement methods based on phase deflection, the present method realizes higher resolution and accuracy of mirror three-dimensional topography measurement effect by using cloud pattern.

[0054] The above specific embodiments can be adjusted in different ways by those skilled in the art without departing from the principles and purposes of the present application, the protection scope of the present application is subject to the claims and is not limited by the above specific embodiments, each implementation scheme within the scope is subject to the present application.

Claims

1. A mirror-based three-dimensional topography measurement system based on projected cloud patterns, characterized in that, include: The system comprises a fringe projection unit, a moiré receiving system unit, and a data processing unit. The fringe projection unit displays a specified fringe pattern on a monitor based on fringe image information sent by a computer and switches the fringe pattern during measurement. The moiré receiving system unit receives the fringe information from the mirror reflection surface, performs geometric interference with a reference grating to form moiré patterns, and captures the resulting moiré pattern using a camera. The data processing unit calculates the three-dimensional morphology of the measured mirror surface based on the obtained moiré pattern information, according to the proposed mirror projection moiré model and mirror moiré morphology solution method. The aforementioned mirror three-dimensional topography measurement refers to: setting a surface light source for displaying stripes at the incident end of the plane to be measured, and setting an optical device, a reference grating, and an image acquisition device at the exit end; and obtaining the three-dimensional topography by projecting a mirror cloud pattern onto the cloud pattern model based on the cloud pattern pattern formed by the interaction of the acquired reflected image of the plane to be measured and the reference grating. The aforementioned specular projection moiré model refers to a model establishing the relationship between the moiré phase, the height of the measured mirror, and the slopes in both directions, using ray tracing and based on the specular reflection theorem. Specifically, it involves using the measured point P and its reflected point B on the display, within a moiré receiving system with an optical center O composed of an output optical device, a reference grating, and an image acquisition device. e Let the coordinates be in the origin coordinate system. Using the law of specular reflection, the relationship between the slope and height of the measured point is established as follows: , , The slopes of the measured point P are given in two directions. The subscript indicates the direction of the slope, and the superscript indicates the object of the slope. , Let P be the pixel coordinates of point P in the reflected image. Here are the coordinates of the principal point of the equivalent image of the moiré receiving system, with the subscript representing the principal point and the superscript representing the moiré receiving system. , The values ​​represent the focal lengths in two directions of the moiré receiving system. The subscript indicates the focal length direction, and the superscript represents the moiré receiving system. , , Let P be the height of the measured point P in the coordinate system of the moiré receiving system. The parameter of the first-order term, , , , , These are combined parameters of the camera parameters and the moiré phase; The combined parameters and the linear term parameters are as follows: , , , , , , , ,in: , The moiré phases in two directions are obtained from actual data acquisition and solution. The subscripts indicate different directions. The coordinates of the principal point of the camera in the image acquisition system. The length of the fringe period of the surface light source. For reference, the grid line spacing, i.e., the period length, , These are the focal lengths of the camera in the x and y directions, with the superscript indicating the camera. , These are the rotation and translation matrices from the raster coordinate system to the camera coordinate system, which are 3x3 and 3x1 matrices respectively. , These are the rotation and translation matrices from the virtual image coordinate system of the surface light source to the equivalent camera coordinate system, respectively, and are matrices of size 3*3 and 3*1.

2. The mirror surface three-dimensional topography measurement system based on projected cloud patterns according to claim 1, characterized in that, The solution for the mirror cloud pattern morphology specifically includes: Step a) Utilizing the assumption of topographic continuity, the relationship between the height and slope of adjacent measured points is introduced, i.e., the Southwell model, specifically: ,in: and For the first in the region of interest Line number List the coordinates and slope of the measured point. , This represents the number of rows and columns of the measured points in the region of interest. Step b) Using moiré data from two locations, at any measured point height... To optimize the variables, with the goal of minimizing the distance, specifically: ,in: and The three-dimensional point cloud coordinate data of the cloud patterns displayed by two surface light sources at two positions, after assuming the same height of the measured point; Step c) When the distance is minimized, the point cloud formed by the coordinates of the measured points obtained at any light source position is the final three-dimensional topographic data of the measured mirror obtained by the method.

3. The mirror surface three-dimensional topography measurement system based on projected moiré patterns according to claim 1 or 2, characterized in that, The aforementioned three-dimensional topography measurement of the mirror surface specifically includes: Step 1) Adjust the receiving system settings: Adjust the focusing ring of the imaging lens so that the focusing ring number is close to the distance between the receiving system and the mirror being measured; adjust the focal length of the imaging lens so that the target area being measured occupies a suitable size in the image captured by the camera; adjust the focal length of the camera lens so that the camera can clearly image the pattern of the position of the mirror being measured. Step 2) Calibrate the equivalent camera's intrinsic parameters, the reference mirror, and the extrinsic parameters corresponding to the first position of the display: Use the display to show the checkerboard calibration plate, change the position and orientation of the calibration plate multiple times, and take pictures of the corresponding checkerboard pattern to calibrate the equivalent camera's intrinsic parameters; Select a position near the mirror being measured as the reference mirror position, place the calibration plate at this position, and take pictures of the checkerboard pattern to calibrate the equivalent camera's extrinsic parameters corresponding to the reference mirror; Select a suitable display measurement position so that the stripe pattern on the display is reflected by the mirror being measured and then captured by the receiving system; Place the standard plane mirror at the aforementioned determined reference mirror position, and place the display at the confirmed measurement position, and use the receiving system to capture the checkerboard pattern of the virtual image on the display within the reference mirror to calibrate the extrinsic parameters corresponding to the virtual image position on the display; Step 3) Capture the cloud-like image of the monitor from its first position: Based on the thickness of the stripes, select a grating with a frequency close to that in the image as a reference grating. Adjust the position of the moving platform so that the grating is located at the focal plane of the camera, forming a clear cloud-like pattern with the stripes; capture the horizontal and vertical phase differences of the monitor under the tested mirror. Each of the four stripe patterns has a phase difference. The cloud pattern formed by the four reference grid patterns; Step 4) Capture the cloud-like pattern image under the second position of the monitor: Move the monitor position so that the stripe pattern received by the receiving system still covers the measurement area of ​​the mirror under test and forms a clear cloud pattern with the reference grid; capture four horizontal and four vertical stripe patterns under the second position of the monitor under the mirror under test. Each pattern corresponds to the phase difference. The cloud pattern formed by the four reference grid patterns; The second position refers to any position on the display in the image where the same display stripes can still cover the tested mirror surface and form clear cloud patterns with the grating. Step 5) Calibrate the extrinsic parameters corresponding to the second position of the display and the camera parameters in the receiving system: Replace the mirror under test with the reference mirror, display the same checkerboard pattern as previously calibrated, and the receiving system takes pictures of the checkerboard pattern of the calibration plate under the reference mirror to calibrate the equivalent camera extrinsic parameters corresponding to the second position of the display; replace the reference grid with the calibration plate and take pictures of the checkerboard pattern at the reference grid position to calibrate the camera extrinsic parameters corresponding to the reference grid; change the pose of the calibration plate and take multiple pictures of the checkerboard pattern to calibrate the camera intrinsic parameters; Step 6) Using the mirror projection cloud pattern model and the mirror cloud pattern morphology solution method, the three-dimensional morphology of the mirror is solved by using the cloud pattern phase.

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