Mirror surface three-dimensional shape measurement method based on projection moire

Abstract

A mirror surface three-dimensional shape measurement method based on projection moire is characterized in that a surface light source used for displaying stripes is arranged at the incident end of a plane to be measured, an optical device, a reference grating and an image acquisition device are arranged at the emergent end, and the three-dimensional shape of the mirror surface is measured according to a moire pattern formed by the action of an acquired reflection image of the plane to be measured and the reference grating. And through the mirror projection moire model, solving the mirror moire morphology to obtain a three-dimensional morphology. By changing a light source, a measurement model, a calibration process and a morphology solving method, the problem of height-gradient ambiguity existing in a single-camera single-display system is solved, and meanwhile, full-field three-dimensional morphology high-resolution measurement of a free mirror surface with the resolution superior to 1 micron can be realized.

Description

Technical Field

[0001] The present invention relates to a technology in the field of three-dimensional shape measurement, in particular to a method for measuring the three-dimensional shape of a mirror surface based on projection moiré. Background Art

[0002] Existing mirror three-dimensional morphology measurement technologies are mostly based on interferometry, which requires complex and precise experimental equipment and a harsh experimental environment. Most of them are only applicable to the morphology measurement of regular mirrors / mirror-like surfaces, and cannot meet the requirements of batch full-field high-precision detection of free mirror morphology in industrial production. Summary of the invention

[0003] In view of the shortcomings of the existing adaptive projection moiré technology for continuous surfaces, which is only applicable to surface diffuse reflection and the reflected light intensity in all directions is almost consistent, and cannot be applied to the measurement of mirror surface morphology, the present invention proposes a mirror three-dimensional morphology measurement method based on projection moiré. By changing the light source, measurement model, calibration process and morphology solution method, the height-gradient ambiguity problem existing in the single-camera single-display system is solved, and the full-field three-dimensional morphology high-resolution measurement of the free mirror with a resolution better than 1 micron can be achieved.

[0004] The present invention is achieved through the following technical solutions:

[0005] The present invention relates to a method for measuring the three-dimensional shape of a mirror surface based on projected moire. A surface light source for displaying stripes is arranged at the incident end of a plane to be measured, and an optical device, a reference grid and an image acquisition device are arranged at the output end. According to the moire pattern formed by the collected reflection image of the plane to be measured and the reference grid, a mirror surface projected moire model is used to obtain the three-dimensional shape through the mirror surface moire shape solution.

[0006] The mirror projection moire model refers to a relationship model between the moire phase, the height of the measured mirror and the slopes in two directions established by using a ray tracing method based on the mirror reflection theorem, specifically: using the measured point P and the point B on the display reflected by it at the optical center O of the moire receiving system composed of the optical device at the output end, the reference grid and the image acquisition device e is the coordinate in the origin coordinate system, and the relationship between the slope of the measured point and the height of the measured point is established by the law of mirror reflection: in: are the two-direction slopes of the measured point P, the subscript represents the direction of the slope, the superscript represents the object of the slope, U and v are the pixel coordinates of point P in the reflected image, is the coordinate of the principal point of the equivalent image of the moiré receiving system, the subscript represents the principal point, and the superscript represents the moiré receiving system. is the focal length of the moiré receiving system in two directions, the subscript represents the focal length direction, the superscript represents the moiré receiving system, σ2, σ3, σ4 are the heights of the measured point P in the coordinate system of the moiré receiving system The first-order parameters of , σ1, σ5, σ6, σ7, σ8 are the combined parameters of the camera parameters and the moiré phase.

[0007] The combined parameters described can all be obtained through calibration and actual measurement.

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

[0009]

[0010]

[0011]

[0012]

[0013]

[0014]

[0015]

[0016]

[0017] Where: φ x ,φ y The moiré phases in two directions are actually collected and solved. The subscripts represent different directions. is the initial phase value of the fringe of the surface light source, is the initial value of the reference grid phase, is the coordinate of the camera principal point in the image acquisition system, p1 is the period length of the surface light source stripe, p2 is the reference grating line distance (period length), is the focal length of the camera in the x and y directions, and the superscript represents the camera. The rotation matrix and translation matrix from the grating coordinate system to the camera coordinate system are 3*3 and 3*1 matrices respectively. They 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 moiré morphology solution specifically includes:

[0019] Step 1) Using the morphology continuity assumption, the relationship between the height and slope of adjacent measured points is introduced, namely the Southwell model, which is specifically: in: and are the coordinates and slopes of the measured point in the i-th row and j-th column 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 moiré data at two locations, the height of any measured point To optimize the variables, the goal is to minimize the distance, specifically: in: and It is the three-dimensional point cloud coordinate data obtained by assuming the same height of the measured point for the moiré pattern displayed by the two-position area light source.

[0021] Step 3) When the distance is minimized, the point cloud composed of the coordinates of the measured points obtained under the position of the light source on any side is the three-dimensional morphology data of the measured mirror surface finally measured by the method.

[0022] The present invention relates to a system for realizing the above method, comprising: a fringe projection unit, a moiré receiving system unit and a data processing unit, wherein: the fringe projection unit displays a specified fringe pattern on a display according to fringe image information sent by a computer, and realizes the switching of fringe patterns during the measurement process; after receiving the fringe information on the mirror reflection surface, the moiré receiving system unit generates geometric interference on a reference grid to form moiré, and the formed moiré pattern is collected by a camera; the data processing unit calculates the three-dimensional morphology result of the measured mirror according to the obtained moiré pattern information, the proposed mirror projection moiré model and the mirror moiré morphology solution method. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 It is a schematic diagram of the structure of the present invention;

[0024] In the figure: display 1, mirror to be tested 2, imaging lens 3, displacement platform and grating 4, housing 5, camera 6, control module 7;

[0025] Figure 2 This is a schematic diagram of the mirror projection moiré model;

[0026] Figure 3 A diagram illustrating the implementation scenario for the example;

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

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

[0029] Figure 5 To measure the images and data related to the concave mirror;

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

[0031] Figure 6 is the measurement result of the concave mirror;

[0032] In the figure: (a) is the three-dimensional morphology of the concave mirror obtained by measurement, (b) is the residual distribution of the measurement result, and (c) is the comparison curve between the lowest contour line of the measurement result and the standard value and the existing method. DETAILED DESCRIPTION

[0033] like Figure 1 , Figure 2 and Figure 3 As shown, the present embodiment relates to a projection moiré system for a continuous mirror, comprising: a display 1 as a surface light source, a mirror 2 to be measured, a receiving system including an imaging lens 3, a grating 4, a housing 5, a camera 6, and a control module 7 for sending and receiving signals, wherein: the control module 7 sends fringe image information to be displayed to the display 1, sends a signal of a moving grating to a displacement platform and a displacement platform in the grating 4, receives the moiré image information recorded by the camera 6, and finally obtains the three-dimensional morphology of the mirror 2 to be measured by image processing calculation.

[0034] In this embodiment, the resolution of the display is 2388*1668, which is used to project the stripe pattern.

[0035] In this embodiment, the imaging lens 3 is a zoom telephoto lens but not limited to it, which is used to receive the stripe pattern reflected by the mirror and converge it on the grating. The imaging lens 3 is fixed on the housing 5 through a dedicated bayonet.

[0036] The displacement platform and grating 4 include: a piezoelectric ceramic displacement platform and a machine-engraved grating. The piezoelectric ceramic displacement platform is a two-dimensional displacement platform, which can achieve a movement with a positioning accuracy of 3nm in two directions in the grating plane; the machine-engraved grating selects a suitable grating pitch and area according to actual measurement requirements, and its function is to generate geometric interference with the mirror fringe pattern converged on the grating to form a moiré pattern.

[0037] In this embodiment, the resolution of the camera 6 is 5472*3648, which is used to collect moiré images.

[0038] The control module 7 is connected to the display 1, the camera 6 and the displacement platform controller respectively to realize fringe image display, moiré image acquisition and displacement platform control, and to process the acquired moiré image to calculate the three-dimensional morphology data of the mirror surface 2 to be measured.

[0039] like Figure 4As shown, the mirror three-dimensional shape measurement method based on projection moiré based on the above system in this embodiment specifically includes:

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

[0041] Step 2) Calibrate the equivalent camera intrinsic parameters, the reference mirror, and the external parameters corresponding to the first position of the display: use the display to display the checkerboard calibration plate, change the position and posture of the calibration plate multiple times, and shoot the corresponding checkerboard pattern for calibrating the equivalent camera intrinsic parameters; select a position near the measured mirror as the reference mirror position, place the calibration plate at this position to shoot the checkerboard pattern, which is used as the extrinsic parameter of the equivalent camera corresponding to the calibration reference mirror; select a suitable display measurement position so that the striped pattern of the display can be reflected by the measured mirror and then photographed by the receiving system; place the standard plane mirror at the reference mirror position determined above, 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 in the reference mirror for calibrating the external parameters corresponding to the virtual image position of the display.

[0042] The equivalent camera is a moiré receiving system. It has been proven that the moiré receiving system can be regarded as an inverted image camera during the calibration process.

[0043] Step 3) photographing a moiré image of the display at the first position: selecting a grating with a close frequency in the image as a reference grating according to the thickness of the stripes, adjusting the position of the mobile platform so that the grating is located at the focal plane of the camera to form a clear moiré pattern with the stripes; photographing four stripe patterns with a horizontal and vertical phase difference of π / 4 on the display under the measured mirror, and forming a moiré pattern with each pattern and four reference grating patterns with a phase difference of π / 4.

[0044] Step 4) photographing a moiré image at the second position of the display: moving the display position so that the display stripe pattern received by the receiving system can still cover the measurement area of ​​the measured mirror and form a clear moiré with the reference grating; photographing a moiré pattern formed by four horizontal and vertical stripe patterns at the second position of the display under the measured mirror and four reference grating patterns with a phase difference of π / 4.

[0045] The second position refers to any display position in the image where the same display stripe can still cover the measured mirror surface and form a clear moiré with the grating.

[0046] Step 5) Calibrate the external parameters corresponding to the second position of the display and the camera parameters in the receiving system: replace the measured mirror with the reference mirror, the display shows the same checkerboard pattern as the previous calibration, and the receiving system photographs the checkerboard pattern of the calibration plate under the reference mirror to calibrate the equivalent camera external parameters corresponding to the second position of the display; replace the reference grid with the calibration plate, photograph the checkerboard pattern at the reference grid position to calibrate the camera external parameters corresponding to the reference grid; change the calibration plate posture, and photograph multiple checkerboard patterns to calibrate the camera intrinsic parameters.

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

[0048] Step 6) Using the mirror projection moiré model and the mirror moiré morphology solution method, the moiré phase is used to solve the mirror three-dimensional morphology.

[0049] After specific actual experiments, based on the projection moiré method for continuous mirrors of the above system, sinusoidal fringes are projected onto the surface of the measured mirror through the display 1 as a surface light source, and after mirror modulation and reflection, they enter the receiving system and interact with the grating to form moiré, which is recorded by the camera 6. In order to facilitate the measurement of measurement errors, the measured mirror uses a concave mirror with a curvature radius of 51.20mm. The mean absolute error (MAE) of the contour line calculated by the mirror projection moiré method of the present invention is 0.0019mm, and the MAE of the contour line calculated by the existing monocular single-screen phase deflectometry is 0.0073mm. The specific experimental data are as follows: Figure 6 And as shown in Table 1.

[0050] Table 1 corresponds to Figure 6 Data (partial)

[0051] In summary, compared with the existing technology, this method constructs a mirror projection moiré model and solves the mirror moiré morphology, and uses the display as a surface light source, so that the projection moiré technology can be used to measure the three-dimensional morphology of the mirror; compared with other existing mirror three-dimensional morphology measurement methods based on phase deflectometry, this method uses moiré to achieve higher resolution and accuracy of mirror three-dimensional morphology measurement effect.

[0052] The above-mentioned specific implementation can be partially adjusted in different ways by those skilled in the art without departing from the principle and purpose of the present invention. The protection scope of the present invention shall be based on the claims and shall not be limited by the above-mentioned specific implementation. Each implementation scheme within its scope shall be subject to the constraints of the present invention.

Claims

1. A method for measuring the three-dimensional shape of a mirror surface based on projected moiré, characterized in that: A surface light source for displaying fringes is arranged at the incident end of the plane to be measured, and an optical device, a reference grid and an image acquisition device are arranged at the output end. According to the moiré pattern formed by the collected reflected image of the plane to be measured and the reference grid, a moiré model is projected on a mirror, and the three-dimensional morphology is obtained by solving the mirror moiré morphology.

2. The method for measuring the three-dimensional shape of a mirror surface based on projection moiré according to claim 1, characterized in that: The mirror projection moire model refers to a relationship model between the moire phase, the height of the measured mirror and the slopes in two directions established by using a ray tracing method based on the mirror reflection theorem, specifically: using the measured point P and the point B on the display reflected by it at the optical center O of the moire receiving system composed of the optical device at the output end, the reference grid and the image acquisition device e is the coordinate in the origin coordinate system, and the relationship between the slope of the measured point and the height of the measured point is established by the law of mirror reflection: in: are the two-direction slopes of the measured point P, the subscript represents the direction of the slope, the superscript represents the object of the slope, u and v are the pixel coordinates of point P in the reflected image, is the coordinate of the principal point of the equivalent image of the moiré receiving system, the subscript represents the principal point, and the superscript represents the moiré receiving system. is the focal length of the moiré receiving system in two directions, the subscript represents the focal length direction, the superscript represents the moiré receiving system, σ2, σ3, σ4 are the heights of the measured point P in the coordinate system of the moiré receiving system The first-order parameters of , σ1, σ5, σ6, σ7, σ8 are the combined parameters of the camera parameters and the moiré phase.

3. The method for measuring the three-dimensional shape of a mirror surface based on projection moiré according to claim 2 is characterized in that: The combination parameters and first-order parameters are: Where: φ x ,φ y The moiré phases in two directions are actually collected and solved. The subscripts represent different directions. is the initial phase value of the surface light source fringe, is the initial value of the reference grid phase, is the coordinate of the camera principal point in the image acquisition system, p1 is the period length of the surface light source stripe, p2 is the reference grating line distance (period length), is the focal length of the camera in the x and y directions, and the superscript represents the camera. The rotation matrix and translation matrix from the grating coordinate system to the camera coordinate system are 3*3 and 3*1 matrices respectively. They 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.

4. The method for measuring the three-dimensional shape of a mirror surface based on projection moiré according to claim 1, characterized in that: The mirror moiré morphology solution specifically includes: Step a) Using the morphology continuity assumption, the relationship between the height and slope of adjacent measured points is introduced, namely the Southwell model, which is specifically: in: and are the coordinates and slopes of the measured point in the i-th row and j-th column in the region of interest, M and N are the number of rows and columns of the measured points in the region of interest; Step b) Using the moiré data at two locations, the height of any measured point To optimize the variables, the goal is to minimize the distance, specifically: in: and The three-dimensional point cloud coordinate data obtained by assuming the same height of the measured point for the moiré patterns displayed by the two-position area light sources; Step c) When the distance is minimized, the point cloud composed of the coordinates of the measured points obtained at the position of the light source on any side is the three-dimensional shape data of the measured mirror surface finally measured by the method.

5. The method for measuring the three-dimensional shape of a mirror surface based on projection moiré according to any one of claims 1 to 4, wherein: include: Step 1) Adjust the receiving system settings: adjust the imaging lens focus ring so that the focus ring number is close to the distance between the receiving system and the measured mirror surface; Adjust the focal length of the imaging lens so that the target area to be measured occupies a suitable size of the camera's captured image; adjust the focal length of the camera lens so that the camera can clearly image the pattern at the position of the measured mirror surface; Step 2) calibrate the equivalent camera intrinsic parameters, the reference mirror, and the external parameters corresponding to the first position of the display: use the display to display the checkerboard calibration plate, change the position and posture of the calibration plate multiple times, and shoot the corresponding checkerboard pattern for calibrating the equivalent camera intrinsic parameters; select a position near the measured mirror as the reference mirror position, place the calibration plate at this position to shoot the checkerboard pattern, which is used as the equivalent camera external parameter corresponding to the calibration reference mirror; select a suitable display measurement position so that the striped pattern of the display is reflected by the measured mirror and then photographed by the receiving system; place the standard plane mirror at the reference mirror position determined above, 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 in the reference mirror for calibrating the external parameters corresponding to the virtual image position of the display; Step 3) photographing a moire image of the display at the first position: selecting a grating with a close frequency in the image as a reference grating according to the thickness of the stripes, adjusting the position of the mobile platform so that the grating is located at the focal plane of the camera to form a clear moire pattern with the stripes; Photograph the moiré pattern formed by four stripe patterns with a horizontal and vertical phase difference of π / 4 on the display under the measured mirror and four reference grating patterns with a phase difference of π / 4; Step 4) photographing a moiré image of the display at the second position: moving the display position so that the display stripe pattern received by the receiving system still covers the measuring area of ​​the measured mirror surface and forms a clear moiré with the reference grating; photographing a moiré pattern formed by four horizontal and vertical stripe patterns of the display at the second position under the measured mirror surface and four reference grating patterns with a phase difference of π / 4; The second position refers to any position of the display in which the same display stripe can still cover the measured mirror surface in the image and form a clear moiré with the grating; Step 5) calibrate the external parameters corresponding to the second position of the display and the camera parameters in the receiving system: replace the measured mirror with the reference mirror, the display shows the same checkerboard pattern as previously calibrated, and the receiving system shoots the checkerboard pattern of the calibration plate under the reference mirror to calibrate the equivalent camera external parameters corresponding to the second position of the display; Replace the reference grid with the calibration plate, and photograph the checkerboard pattern at the reference grid position to calibrate the reference grid corresponding to the camera extrinsic parameters; Change the calibration plate posture and take multiple pictures of the checkerboard pattern to calibrate the camera intrinsic parameters; Step 6) Using the mirror projection moiré model and the mirror moiré morphology solution method, the moiré phase is used to solve the mirror three-dimensional morphology.

6. A system for measuring the three-dimensional shape of a mirror surface based on projection moiré for implementing any of the methods described in claims 1 to 5, characterized in that: include: A fringe projection unit, a moiré receiving system unit and a data processing unit, wherein: the fringe projection unit displays a specified fringe pattern on a display according to fringe image information sent by a computer, and realizes the switching of fringe patterns during the measurement process; after receiving the fringe information on the mirror reflection surface, the moiré receiving system unit generates geometric interference on a reference grid to form moiré, and the formed moiré pattern is collected by a camera; the data processing unit calculates the three-dimensional morphology result of the measured mirror according to the obtained moiré pattern information, the proposed mirror projection moiré model and the mirror moiré morphology solution method.

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