Three-dimensional measurement method based on multi-step radial structured light and ray conic polar line geometry

Abstract

The application discloses a three-dimensional measurement method based on multi-step radial structured light and ray cone polar line geometry, and relates to the technical field of three-dimensional measurement. The method comprises the following steps: selecting a topological singular point, calculating the gray scale of each pixel through a gray scale distribution function, generating a concentric circular ring multi-step radial phase shift fringe pattern sequence, and sequentially projecting the fringe pattern sequence onto the surface of a measured object; collecting a deformation image sequence; through multi-step phase shift orthogonal operation, calculating the wrapped phase and modulation degree pixel by pixel; taking the topological singular point as an absolute anchor point, taking the modulation degree as a quality guide, unwrapping the wrapped phase through regional growth space to obtain an absolute phase of a full frame, constructing a camera ray, determining a projection cone surface based on the absolute phase, solving the three-dimensional coordinates of a measured point through the space geometry intersection of the camera ray and the projection cone surface, calculating the space geometry residual error of the camera ray and the projection cone surface, eliminating out-of-limit pixels, and obtaining a three-dimensional point cloud. The application can ensure the point cloud integrity and measurement reliability of a key detection area.

Description

Technical Field

[0001] This invention relates to the field of three-dimensional measurement technology, and in particular to a three-dimensional measurement method based on multi-step radial structured light and ray conic polar geometry. Background Technology

[0002] In the fields of semiconductor packaging (such as BGA and wafers), printed circuit boards (PCBA), and automated optical inspection (3D AOI) of precision components, active structured light 3D measurement technology based on digital micromirror devices (DMDs) is widely used. This technology projects an coded structured light pattern onto the surface of the object being measured using a projector, while a camera captures deformed images modulated by the object's surface topography. Then, a specific decoding algorithm and triangulation model are used to convert the phase information in the images into 3D point cloud data.

[0003] Traditional measurement schemes typically use one-dimensional linear phase-shifting fringes (i.e., parallel straight fringes) as the basic coding pattern, and their typical measurement process includes the following steps: Pattern projection stage: The optomechanical system sequentially projects multiple frames of basic phase-shifted fringe patterns onto the object under test (usually 4 steps, with a phase difference of π / 2 between adjacent patterns) to obtain a sinusoidal brightness sequence for solving the wrapped phase; in addition, multiple frames of auxiliary coded patterns are also projected to eliminate the 2π periodic blur of the wrapped phase and determine the absolute fringe period number of each pixel.

[0004] Absolute phase calculation stage: After the camera synchronously acquires all the above patterns, the wrapped phase, whose value range is truncated to the interval (-π,π] or (0,2π], is first calculated from the basic phase-shifted image using the four-step phase-shift formula. Then, with the help of the period number information provided by the auxiliary pattern, the wrapped phase is unfolded into a continuous full-field absolute phase using the time phase unwrapping algorithm. There are two main auxiliary encoding methods: one is to project multiple frames of Gray code patterns (usually 4 to 8 frames), and divide the projected field of view into several non-overlapping encoding regions through black and white binary encoding, with each region corresponding to a unique binary period number; the other is to project multi-frequency heterodyne patterns, that is, to additionally project at least one set of sinusoidal phase-shifted fringes with different spatial frequencies, and use the beat effect between the two sets of wrapped phases with different frequencies to synthesize an equivalent phase with a period sufficient to cover the entire field of view, and then determine the fringe order step by step from coarse to fine.

[0005] 3D Reconstruction Stage: After obtaining the absolute phase, the absolute phase is converted into physical height Z or 3D point cloud coordinates (X, Y, Z) using a pre-calibrated empirical polynomial for phase height mapping or a unidirectional triangulation model based on ray-plane intersection. In the ray-plane model, the camera's outgoing ray is considered a straight line in space, and the equiphase surface determined by the absolute phase is considered a plane. The 3D point is determined by the intersection of the ray and the plane.

[0006] However, the aforementioned traditional linear structured light measurement technology has the following serious drawbacks in practical industrial applications: Measurement cycle time is severely limited. Since one-dimensional linear fringes do not have a physical starting point for distinguishing periods, a large number of auxiliary patterns must be projected to eliminate 2π ambiguity. Taking the "4-step phase shift + 8-frame Gray code" scheme as an example, at least 12 frames of images need to be acquired for a single measurement, which greatly increases the hardware image acquisition time and data processing volume of a single measurement cycle, severely restricting the unit hour output (UPH) of automated production lines.

[0007] The inherent "ripple" noise exists. Traditional 4-step phase-shifting algorithms are extremely sensitive to the gamma nonlinearity of the projector and the quantization error of 8-bit image sampling. Since both digital projection and image acquisition involve discrete quantization processes, high-order harmonics and quantization noise are inevitably mixed into the sinusoidal brightness signal captured by the camera. After these errors are solved by the phase-shifting formula, they appear as periodic "ripple" phase ripples on a smooth surface. After 3D reconstruction, they are transformed into periodic undulations on the point cloud surface, which is difficult to meet the high-precision detection requirements of ±10μm.

[0008] The ray-plane model has weak spatial constraints and is susceptible to multipath reflection interference. The equiphase surface of a traditional linear phase is represented as a plane in 3D space. When a camera ray intersects this plane, it lacks spatial constraints along the fringe direction. When facing highly reflective arrays such as BGA solder balls and metal pads, light may undergo multiple reflections between metal surfaces, creating multipath interference. These spurious reflection signals, once captured by the camera, will calculate incorrect phase values. The ray-plane model almost always finds an intersection point to output 3D coordinates, thus generating severe "flying glitch" or "deep pit" noise, which cannot be effectively identified and removed geometrically.

[0009] It is susceptible to beat frequency interference from orthogonal matrix textures. Test objects such as chip pins and PCBA traces often have regular, grid-like structures with horizontal and vertical lines. When the projected straight stripes are nearly parallel or orthogonal to the direction of these physical textures, the two sets of regular patterns with similar spatial frequencies superimpose on the camera's imaging surface, easily producing moiré fringes. This interference severely damages local phase information, leading to large blind spots or erroneous fluctuations in the reconstructed point cloud in key detection areas.

[0010] In summary, existing one-dimensional linear structured light measurement technology has significant shortcomings in terms of measurement speed, point cloud accuracy, anti-reflection robustness, and anti-texture interference capability. There is an urgent need for a new structured light coding mode and three-dimensional reconstruction architecture to overcome these deficiencies. Summary of the Invention

[0011] This invention provides a three-dimensional measurement method based on multi-step radial structured light and ray conic polar geometry, including: Step S1: Select topological singularities, calculate the gray level of each pixel through the gray level distribution function, generate a sequence of concentric circular multi-step radial phase-shifting stripe patterns, and project them sequentially onto the surface of the object being measured. Step S2: Acquire the deformed image sequence, and calculate the wrapping phase and modulation degree pixel by pixel through multi-step phase-shifting orthogonal operation; Step S3: Using the topological singularity as the absolute anchor point and the modulation degree as the quality guide, the wrapped phase is unwrapped through the region growing space to obtain the absolute phase of the full frame. Step S4: Construct the camera ray and determine the projection cone surface based on the absolute phase. Solve the three-dimensional coordinates of the measured point by finding the intersection of the two in spatial geometry. Step S5: Calculate the spatial geometric residual between the camera ray and the projection cone, remove out-of-limit pixels, and obtain the 3D point cloud.

[0012] The three-dimensional measurement method based on multi-step radial structured light and ray conic epipolar geometry, as described above, involves selecting topological singularities, calculating the grayscale of each pixel using a grayscale distribution function, generating a sequence of concentric annular multi-step radial phase-shifting fringe patterns, and projecting them sequentially onto the surface of the object being measured. This includes the following sub-steps: Step S11: Select a topological singularity in the projector image plane coordinate system and set the encoding parameters. Calculate the grayscale pixel by pixel with radial Euclidean distance as the independent variable to generate a concentric annular multi-step radial phase-shifting stripe pattern sequence. Step S12: Load the radial phase-shifted stripe pattern sequence onto the projection unit in phase-shift order, and project it onto the surface of the object being measured.

[0013] The three-dimensional measurement method based on multi-step radial structured light and ray conic epipolar geometry, as described above, includes the following methods for selecting topological singularities: directly specifying the coordinates of the image plane center, and obtaining sub-pixel-level precise coordinates by projecting a marked pattern, acquiring it by the camera, and then back-calculating it through calibration mapping. The singularity is the geometric center of all concentric ring fringes and the isolated singularity of the phase field.

[0014] The three-dimensional measurement method based on multi-step radial structured light and ray conic epipolar geometry, as described above, involves projecting a crosshair or dot pattern onto a reference plane, extracting the feature point image coordinates after the camera acquires the data, and mapping the feature point coordinates back to the projector image plane coordinate system using the homography matrix obtained through joint calibration of the projector and camera. This process yields the sub-pixel level precise coordinates of the topological singularity.

[0015] As described above, the three-dimensional measurement method based on multi-step radial structured light and ray conic polar geometry involves writing the grayscale data of the radial phase-shifted fringe pattern into the frame buffer of the projection unit in phase-shift order. The digital micromirror device of the projection unit controls the flipping state of each micromirror according to the grayscale data of each frame. After passing through the illumination source and the projection optical system, the pattern is projected onto the surface of the object being measured.

[0016] The three-dimensional measurement method based on multi-step radial structured light and ray conic epipolar geometry, as described above, involves acquiring a sequence of deformed images and calculating the wrapping phase and modulation index pixel-by-pixel through multi-step phase-shift orthogonal operations. This includes the following sub-steps: Step S21: Sequentially acquire deformed images of each pattern modulated by the surface morphology of the object being measured, to obtain a deformed image sequence; Step S22: Based on the deformed image sequence, calculate the sine and cosine components through multi-step phase-shifting orthogonal operations, and solve the wrapping phase and modulation.

[0017] The three-dimensional measurement method based on multi-step radial structured light and ray conic polar geometry, as described above, establishes a hardware synchronous trigger signal path between the projection unit and the image acquisition unit. After the projection unit completes the stable display of each pattern, it sends a trigger signal, and the image acquisition unit performs a synchronous exposure to acquire a frame of deformed image modulated by the surface morphology of the object under test. The patterns are acquired sequentially according to the projection order to obtain a deformed image sequence.

[0018] The three-dimensional measurement method based on multi-step radial structured light and ray conic epipolar geometry, as described above, includes the following sub-steps: Based on a deformed image sequence, the sinusoidal and cosine components are calculated through multi-step phase-shift orthogonal operations to resolve the encapsulation phase and modulation. Step S221: Based on the deformed image sequence, extract the grayscale sequence pixel by pixel, and calculate the sine and cosine components pixel by pixel through multi-step phase-shifting orthogonal operation; Step S222: Calculate the wrapping phase of each pixel based on the sine and cosine components; Step S223: Calculate the modulation index of each pixel based on the sine and cosine components.

[0019] The 3D measurement method based on multi-step radial structured light and ray conical epipolar geometry, as described above, includes the following sub-steps: calculating the spatial geometric residual between the camera ray and the projected conical surface, removing out-of-limit pixels, and obtaining the 3D point cloud. Step S51: Calculate the spatial geometric residual between the camera ray and the projection cone surface; Step S52: Compare the geometric residual with the safety threshold, remove out-of-limit pixels, and obtain a high-fidelity 3D point cloud.

[0020] This invention also provides a three-dimensional measurement system based on multi-step radial structured light and ray conic epipolar geometry, comprising: The phase-shifting fringe pattern sequence generation module selects topological singularities, calculates the gray level of each pixel through a gray-level distribution function, generates a concentric annular multi-step radial phase-shifting fringe pattern sequence, and projects it sequentially onto the surface of the object being measured. The wrapping phase and modulation acquisition module acquires deformed image sequences and calculates the wrapping phase and modulation per pixel through multi-step phase-shift orthogonal operations. The absolute phase acquisition module uses topological singularities as absolute anchor points and modulation as the quality guide. It unwraps the wrapped phase through the region growing space to obtain the absolute phase of the full frame. The 3D coordinate solving module constructs camera rays and determines the projection cone based on the absolute phase. It then solves the 3D coordinates of the measured point by finding the intersection of the two in spatial geometry. The 3D point cloud acquisition module calculates the spatial geometric residual between the camera ray and the projected cone, removes out-of-limit pixels, and acquires the 3D point cloud.

[0021] The beneficial effects achieved by this invention are as follows: This invention significantly improves the production line cycle time for 3D measurement. Only one set of phase-shift patterns is needed to complete the full-field absolute phase acquisition, reducing the number of images acquired per measurement by about one-third compared to traditional methods, and significantly shortening hardware processing time. Furthermore, point cloud accuracy is qualitatively improved, with the modulation range compressed by approximately four orders of magnitude. Quantization noise and periodic ripples introduced by gamma nonlinearity are completely eliminated. The reconstructed surface exhibits extremely high smoothness in both bright and dark areas, meeting the high-precision detection requirements of ±10μm. More importantly, when dealing with highly reflective devices such as metal solder balls and bare dies, the system utilizes geometrical dimensional constraints to physically identify and eliminate false signals generated by multipath reflections, fundamentally avoiding fly-point burrs and deep pit noise that are difficult to detect in traditional methods, outputting high-fidelity 3D point clouds with significantly enhanced robustness. Simultaneously, the concentric ring pattern covers all directions with omnidirectional radiating fringe normals, eliminating moiré fringe interference with orthogonal regular textures at the physical source, ensuring the integrity of the point cloud and the reliability of measurement in key detection areas. Attached Figure Description

[0022] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in the present invention. For those skilled in the art, other drawings can be obtained based on these drawings.

[0023] Figure 1 This is a flowchart of a three-dimensional measurement method based on multi-step radial structured light and ray conic polar geometry provided in Embodiment 1 of this application; Figure 2 This is a schematic diagram of the system hardware architecture and optical path provided in Embodiment 1 of this application; Figure 3 This is the radial eight-step phase shift diagram provided in Embodiment 1 of this application; Figure 4 This is the eight-step phase shift modulation diagram provided in Embodiment 1 of this application; Figure 5 This is a diagram of the four-step phase shift modulation process provided in Embodiment 1 of this application; Figure 6 This is a cross-sectional view of the four-step phase shift modulation process provided in Embodiment 1 of this application; Figure 7 This is a cross-sectional view of the eight-step phase shift modulation regime provided in Embodiment 1 of this application; Figure 8 This is the package phase diagram provided in Embodiment 1 of this application; Figure 9 This is an unwrapping phase cross-sectional view provided in Embodiment 1 of this application; Figure 10 This is the absolute phase diagram unfolded from the center outwards, as provided in Embodiment 1 of this application; Figure 11 It is a pseudo-color image of the absolute phase map provided in Embodiment 1 of this application; Figure 12 This is a three-dimensional diagram of the intersection of ray and conic polar geometry provided in Embodiment 1 of this application. Detailed Implementation

[0024] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0025] Example 1

[0026] like Figure 1 As shown, Embodiment 1 of this application provides a three-dimensional measurement method based on multi-step radial structured light and ray conic polar geometry, which includes the following steps: Step S1: Select topological singularities, calculate the gray level of each pixel through the gray level distribution function, generate a sequence of concentric circular multi-step radial phase-shifting stripe patterns, and project them sequentially onto the surface of the object being measured. like Figure 2 As shown, the projection unit projects concentric circular radial phase-shifted stripe patterns onto the surface of the object being measured in sequence, while the image acquisition unit simultaneously acquires deformed images from another angle, forming a triangulation measurement optical path.

[0027] Furthermore, topological singularities are selected, and the gray levels of each pixel are calculated using a gray-level distribution function to generate a sequence of concentric circular multi-step radial phase-shifting fringe patterns, which are then sequentially projected onto the surface of the object under test, including the following sub-steps: Step S11: Select a topological singularity in the projector image plane coordinate system and set the encoding parameters. Calculate the grayscale pixel by pixel with radial Euclidean distance as the independent variable to generate a concentric annular multi-step radial phase-shifting stripe pattern sequence. Specifically, pixel coordinates are selected in the image plane coordinate system of the digital micromirror device of the projector. As a topological singularity, the selection methods for the topological singularity include directly specifying the coordinates of the image plane center, and obtaining sub-pixel-level precise coordinates by projecting a marked pattern and acquiring it by the camera, followed by calibration mapping and back-calculation. The singularity is the isolated singularity of the geometric center of all concentric ring fringes and the phase field. The calibration mapping and back-calculation method involves projecting a crosshair or dot marked pattern onto a reference plane, acquiring it by the camera, extracting the feature point image coordinates, and mapping the feature point coordinates back to the projector image plane coordinate system through the homography matrix obtained by the projector-camera joint calibration, thereby obtaining the sub-pixel-level precise coordinates of the topological singularity.

[0028] The radial pixel width of the projector image plane is determined based on the size of the object being measured and the camera's field of view. The initial value of the number of pixels per period is calculated based on the total number of required fringe periods. The phase shift step number N is set, where N is an integer not less than 6. To ensure that the phase step of each of the N phase shift steps can be accurately resolved by the DMD (Digital Micromirror Device), the lower limit of the number of pixels occupied by a single period is set to N pixels in the entire effective measurement area. At the same time, based on the camera's imaging resolution, the lower limit of the number of pixels occupied by a single period is set to 4 pixels after conversion to the camera image plane. This lower limit is set based on the Nyquist sampling theorem, which requires at least 2 pixels to be sampled for each sinusoidal fringe period at the camera end. Considering the image edge blurring effect caused by the point spread function of the optical system, in order to ensure the phase restoration accuracy of the sinusoidal waveform, it is usually required that the number of pixels per period be no less than 4 pixels in engineering practice. Based on the above constraints, the physical period P of the radial stripes is determined. The physical period P is defined as the radial linear physical distance equivalent corresponding to the radial phase change of 2π on the physical target surface of the projector DMD. In actual encoding, this physical distance equivalent is discretely taken in units of the number of pixels on the projected image surface. Once set, it remains unchanged throughout the entire measurement process.

[0029] The larger N is, the narrower the bandpass characteristic of the phase-shift orthogonal basis function in the frequency domain, and the more higher-order harmonics can be filtered out. However, the number of images acquired also increases, and the measurement cycle time decreases accordingly. Under the combined effect of DMD 8-bit discrete quantization and projector gamma nonlinearity, the fringe images acquired by the camera contain second to seventh-order higher-order harmonic components. According to the harmonic filtering rules of the N-step phase-shift method, N-step phase shift can effectively filter out higher-order harmonics below N+1. When N<8, some harmonics cannot be completely filtered out by the phase-shift orthogonal operation, and weak water ripple noise will still remain in the point cloud. When N=8, all higher-order harmonics from the second to the seventh can be completely filtered out, leaving only the fundamental frequency component, and completely isolating the aliasing of quantization noise and phase signal at the algebraic level. When N>8, although higher-order harmonics can be filtered out, the number of images acquired increases, which seriously slows down the measurement cycle time. Moreover, under 8-bit quantization conditions, the energy of harmonics above the ninth order is already extremely low, and the marginal benefit of further increasing the number of steps is minimal. Preferably, when N=8, the phase shift amount , The corresponding period constraints are that the single period at the DMD end is not less than 8 pixels and the single period at the camera end is not less than 4 pixels.

[0030] For any pixel in the projector image plane ,pass calculate To topological singularity The radial Euclidean distance, in As the independent variable, through the grayscale distribution function Calculate the first pixel The grayscale values ​​of the step pattern, where, for The first The grayscale values ​​of the step pattern are: A is the DC component of the background light intensity, and B is the modulation amplitude. The physical period of the radial stripes. for To topological singularity The radial Euclidean distance, For the first The phase shift of the step, when N=8, After pixel-by-pixel calculation as described above, N grayscale patterns are generated, presenting a concentric ring distribution centered on the topological singularity, with alternating light and dark areas along the radial direction and a constant physical period. When N=8, the generated radial eight-step phase-shift patterns I1~I8 are as follows: Figure 3 As shown.

[0031] Step S12: Load the radial phase-shifted fringe pattern sequence onto the projection unit in phase-shift order, and project it onto the surface of the object being measured in sequence; Specifically, the grayscale data of N radial phase-shifted fringe patterns are written into the frame buffer of the projection unit in phase shift order. The digital micromirror device of the projection unit controls the flipping state of each micromirror according to the grayscale data of each frame. After passing through the illumination source and the projection optical system, the pattern is projected onto the surface of the object being measured.

[0032] Step S2: Acquire the deformed image sequence, and calculate the wrapping phase and modulation degree pixel by pixel through multi-step phase-shifting orthogonal operation; Furthermore, a sequence of deformed images is acquired, and the wrapping phase and modulation are calculated pixel by pixel through multi-step phase-shift orthogonal operations, including the following sub-steps: Step S21: Sequentially acquire deformed images of each pattern modulated by the surface morphology of the object being measured, to obtain a deformed image sequence; Specifically, a hardware synchronization trigger signal path is established between the projection unit and the image acquisition unit. After the projection unit completes the stable display of each pattern, it sends a trigger signal, and the image acquisition unit performs a synchronous exposure to acquire a frame of deformed image modulated by the surface morphology of the object under test. N patterns are acquired in sequence according to the projection order to obtain a sequence of N deformed images.

[0033] Step S22: Based on the deformed image sequence, calculate the sine and cosine components through multi-step phase-shifting orthogonal operations, and solve the wrapping phase and modulation. Furthermore, based on the deformed image sequence, the sinusoidal and cosine components are calculated through multi-step phase-shifting orthogonal operations to solve for the encapsulation phase and modulation, including the following sub-steps: Step S221: Based on the deformed image sequence, extract the grayscale sequence pixel by pixel, and calculate the sine and cosine components pixel by pixel through multi-step phase-shifting orthogonal operation; Specifically, for each pixel position in the deformed image, the corresponding grayscale value sequence in N frames of the deformed image is extracted. When N=8, the grayscale value sequence is denoted as... The subscripts correspond to the phase shift sequence numbers. Through the 8-step phase-shift orthogonal decomposition formula Calculate the sine component Y and cosine component X of the corresponding pixel, where c is a constant. In the above formula, the combination of gray values ​​corresponds to the symmetrical distribution of the 8 phase-shift sampling points on the unit circle. The 8 sampling points are located at 0°, 45°, 90°, 135°, 180°, 225°, 270°, and 315°, respectively. and Located in the 0° and 180° axial directions, and Located in the 90° and 270° axial directions, These are located at diagonal angles of 45°, 135°, 225°, and 315°, respectively. The coefficient of contribution from axial sampling points during orthogonal projection is naturally 1, while the coordinate components of diagonal sampling points projected onto the horizontal or vertical axis are... ,constant The function is to assign weights to the sampling points along the four diagonal directions that match the coordinate components of the unit circle, ensuring that the contribution of each sampling point in the orthogonal projection direction is strictly consistent with the coordinate components on the unit circle. Through this weighted combination, the sine component Y responds only to the fundamental frequency sine component, the cosine component X responds only to the fundamental frequency cosine component, and the DC component and the second to seventh harmonic components are completely canceled out during the algebraic summation process, achieving precise filtering of each order of harmonics at the algebraic level.

[0034] When N takes other values, the calculation of the sine component Y and the cosine component X adopts the general N-step phase shift formula corresponding to the number of steps, which is consistent with the case when N=8. In both cases, the gray-scale sequence is subjected to inner product operation with the sine template and the cosine template respectively to extract the fundamental frequency component.

[0035] Step S222: Calculate the wrapping phase of each pixel based on the sine and cosine components; Specifically, based on the sine component Y and the cosine component X, through Calculate the wrap phase of each pixel , wrap phase The range of values ​​is truncated to Within the interval, a jump from π to -π occurs when crossing different fringe periods, forming a periodic wrapping that envelops the phase. Stored as a two-dimensional matrix with the same resolution as the acquired image.

[0036] Step S223: Calculate the modulation index of each pixel based on the sine and cosine components; Specifically, based on the sine component Y and the cosine component X, through Calculate the modulation degree M for each pixel. The modulation degree M represents the signal-to-noise ratio of the stripe signal at that pixel and the reliability of the phase calculation. The higher the modulation degree, the stronger the contrast of the stripes acquired by that pixel and the more reliable the phase calculation result. The lower the modulation degree, the more reliable the phase calculation result. The modulation degree M is stored as a two-dimensional matrix with the same resolution as the acquired image.

[0037] like Figure 4 , 5As shown in Figures 6 and 7, a comparison of the modulation schemes of 8-step and 4-step phase shifts reveals that the modulation scheme of the 8-step phase shift is more uniformly distributed with a flat profile, while the modulation scheme of the 4-step phase shift exhibits significant periodic fluctuations. The modulation scheme range of the 4-step phase shift is 126.253571~127.739541, with a modulation scheme range of 1.48597. In contrast, the modulation scheme range of the 8-step phase shift is 127.471298~127.471340, with a modulation scheme range of 0.000042, representing a compression of approximately four orders of magnitude. This demonstrates that the 8-step radial phase shift encoding and decoding exhibits superior anti-quantization capabilities compared to the traditional 4-step phase shift, demonstrating stronger anti-quantization performance in both encoding and decoding.

[0038] Step S3: Using the topological singularity as the absolute anchor point and the modulation degree as the quality guide, the wrapped phase is unwrapped through the region growing space to obtain the absolute phase of the full frame. Furthermore, using the topological singularity as the absolute anchor point and modulation as the quality guide, the wrapped phase is unwrapped through the region growing space to obtain the absolute phase of the full frame, including the following sub-steps: Step S31: Map the topological singularity to the deformed image, determine the absolute anchor point position, and assign an initial absolute phase value; Specifically, based on the pre-calibrated mapping relationship between the projector and the camera, the coordinates of the topological singularity selected in the projector image plane coordinate system will be... Transform to the camera image plane coordinate system to determine the corresponding pixel position of the topological singularity in the deformed image. Use this position as the absolute anchor point for phase unfolding, and denote the pixel of this anchor point as... In the absolute phase map, assign anchor pixel. Initial absolute phase value ,in, As a preset constant, it is usually taken as ,Will Marked as expanded pixels.

[0039] Step S32: Using modulation as the quality guide, grow pixel by pixel from the absolute anchor point and iteratively expand to obtain the absolute phase of the full frame; Specifically, the modulation degree M is used as the quality measure of each pixel. Based on the system noise floor and the lowest resolvable contrast of the stripe signal, a modulation degree threshold is set. Pixels with a modulation degree M greater than the threshold are determined to be valid pixels, while pixels with a modulation degree M lower than the threshold are considered unreliable regions and are not included in the unfolding.

[0040] Establish a priority queue of pixels to be expanded. Pixels in the queue are sorted from highest to lowest modulation level M, with higher modulation levels indicating higher priority, and are dequeued and expanded first. Initially, anchor points are used... Centered on the target, examine all adjacent valid pixels in its neighborhood that are not marked as expanded, and insert each adjacent valid pixel into the priority queue in descending order of its modulation degree M.

[0041] The pixel with the highest modulation intensity is retrieved from the priority queue and designated as the current pixel to be expanded, denoted as p. The neighboring pixels of p that have already been expanded are identified and denoted as q. If multiple expanded pixels exist in the neighborhood, the pixel with the highest modulation intensity M is selected as q. The absolute phase value of q is then obtained. Based on the premise that the true phase of adjacent pixels is continuous, the unwrapping formula is used. Calculate the absolute phase of pixel p ,in, Let p be the wrapping phase. Let p be the absolute phase of pixel p, and k be the stripe period compensation coefficient. This represents the rounding function, used to determine... Compared to Does a jump that is an integer multiple of 2π exist, and determine the compensation amount, when the difference between the two is within... Within the interval, k=0, which is equivalent to directly using the wrapped phase as the absolute phase. When the difference exceeds this interval, k takes the required integer value such as ±1 or ±2, and after compensation, makes... and Continuous. Mark pixel p as an expanded pixel, and insert the adjacent valid pixels of p that have not been marked as expanded into the priority queue in descending order of their modulation M.

[0042] Repeat the above dequeue determination, compensation, and enqueue operation until all valid pixels are marked as unfolded, obtaining a full-frame continuous absolute phase map. In this system, the absolute phase value of each valid pixel is uniquely determined, and there is no 2π-integer multiple blur.

[0043] like Figure 8 As shown, the wrapping phase diagram exhibits a concentric ring distribution that periodically wraps outward from the central singularity, as... Figure 9 and 10 As shown, the unwrapped phase profile reveals that the phase monotonically increases from the center outwards. The full-field absolute phase map obtained after region growing and unfolding exhibits a smooth and continuous central radial distribution, as shown in the figure. Figure 11 As shown, the pseudo-color image visually demonstrates the spatial characteristic of the absolute phase monotonically increasing outward from the center zero point.

[0044] Step S4: Construct the camera ray and determine the projection cone surface based on the absolute phase. Solve the three-dimensional coordinates of the measured point by finding the intersection of the two in spatial geometry. like Figure 12 As shown, the camera ray originates from the camera optical center. Starting from the point corresponding to the pixel in space, the projected cone surface is about the optical center of the projector. With the vertex as the vertex and the projector's optical axis as the central axis, the half-angle of the ray is determined by the absolute phase. The intersection of the ray and the conical surface is the three-dimensional spatial position of the measured point. This constitutes a geometric intersection model of ray and conic polar line.

[0045] Furthermore, the camera ray is constructed, and the projection cone is determined based on the absolute phase. The three-dimensional coordinates of the measured point are then solved by finding the intersection of the two in spatial geometry, including the following sub-steps: Step S41: Based on the camera intrinsic parameters, back-project the pixel coordinates to construct a camera ray in the world coordinate system; Specifically, for any valid pixel in the deformed image, its pixel coordinates in the camera image plane coordinate system are denoted as... Based on the pre-calibrated camera intrinsic parameter matrix and distortion coefficients, the pixel coordinates are... Distortion correction is performed to obtain the corrected pixel coordinates. Based on the camera intrinsic parameter matrix, the corrected pixel coordinates are transformed to a normalized plane coordinate system to obtain the coordinates of the pixel in the normalized plane. .

[0046] In the world coordinate system, with the camera optical center As the starting point of the ray, Pointed by the optical center of the camera to a point on the normalized plane Direction vector corresponding to spatial direction The direction of the ray. Construct the camera ray corresponding to this pixel. ,in, Indicates camera ray, Let be the optical center of the camera, and t be the depth parameter, representing the distance from the optical center of the camera along the direction of the light ray. , direction vector It is obtained by transforming normalized planar coordinates to the world coordinate system using the camera rotation matrix and then normalizing them.

[0047] Step S42: Based on the absolute phase, calculate the radial radius on the projector image plane, and determine the projection cone surface by combining the projector optical center; Specifically, based on pixels absolute phase With the radial fringe physical period P, through Inverse pixel calculation The radial radius of the concentric rings corresponding to the absolute phase value on the image plane of the projector's digital micromirror device, where, The radial radius of the concentric rings represents the pixel. The corresponding equiphase lines are located on the projector image plane at a distance from the topological singularity. radial pixel distance, For pixels The absolute phase value, P is the physical period of the radial stripe.

[0048] Based on the intrinsic parameter matrix obtained from the projector calibration, the radius on the projected image surface is... The annular mapping is from the projector optical center A group of emitted space rays, Since every point on the annulus is equidistant from the topological singularity, this set of rays is parallel to the projector's optical axis. The included angles are all equal, and are denoted as half an angle. Half angle pass It is confirmed that, among them, This is the focal length in the projector's intrinsic parameters, expressed in pixels.

[0049] The aforementioned set of spatial rays together spans in three-dimensional space to form an optical axis centered on the projector. With the vertex as the point of view and the projector's optical axis as the reference point... The equation of the conical surface with the central axis as its center is: ,in, For projector optical core Coordinates in the world coordinate system For the absolute phase The modulated tangent of the cone half-angle, i.e. .

[0050] Step S43: Based on the camera ray and the projection cone, calculate the depth parameters and obtain the three-dimensional coordinates of the measured point; Specifically, corresponding pixels Camera rays Expand into components and substitute them into the equation of the quadratic surface of the projected cone. The simultaneous equations are transformed into a quadratic equation in one variable with respect to the parameter t. ,in, Let be the coordinates of the camera's optical center in the world coordinate system. Let be the coordinates of the projector's optical center in the world coordinate system. These are the three components of the camera ray direction vector. For the absolute phase The modulated cone half-angle tangent is used to solve the above quadratic equation to obtain real roots. From the obtained roots, the real roots that are located within the effective depth range of the measurement system are selected as the effective depth parameter. The effective depth of field is predetermined by the working distance and depth parameters of the measurement system. When two real roots are both within the effective depth of field, one is selected based on the continuity of the object's surface or other prior information; typically, the smaller depth value corresponds to the front surface of the object. When no real roots are within the effective depth of field, it indicates that the measurement result corresponding to that pixel is geometrically invalid and is marked accordingly.

[0051] Effective depth parameters Substitute camera ray Obtain the three-dimensional coordinates of the measured point corresponding to the pixel in the world coordinate system. .

[0052] Step S5: Calculate the spatial geometric residual between the camera ray and the projected cone, remove out-of-limit pixels, and obtain the 3D point cloud; Further, the spatial geometric residual between the camera ray and the projected cone is calculated, out-of-limit pixels are removed, and a 3D point cloud is obtained, including the following sub-steps: Step S51: Calculate the spatial geometric residual between the camera ray and the projection cone surface; Specifically, when a pixel is marked, the reprojection geometric residual of that pixel is assigned a preset value greater than the safety threshold, and the process proceeds directly to step S52.

[0053] For unmarked pixels, the projection cone surface corresponding to the pixel is discretized into a set of generatrices. The generatrices are straight lines on the cone surface that start from the optical center of the projector and run along different azimuth angles. With the optical axis of the projector as the central axis, the generatrices are uniformly sampled within the azimuth angle range of 0 to 360 degrees according to a preset angle step size to generate a set of generatrices direction vectors. The angle between the direction vector of each generatrices and the optical axis of the projector is always equal to half the cone angle.

[0054] For each generatrix, calculate the spatial distance between the camera ray and the corresponding generatrix. The shortest distance between two spatial lines is the length of their common perpendicular. The calculation method is to find the direction vector of the common perpendicular that is perpendicular to both the direction vector of the camera ray and the direction vector of the generatrix, and then calculate the projection length of the vector from the optical center of the camera to the optical center of the projector in the direction of the common perpendicular. The absolute value of this projection length is the shortest distance between the two lines.

[0055] By traversing the generatrix of all sampled azimuth angles, a set of distance values ​​is obtained. The minimum value in this set of distance values ​​is taken as the shortest spatial distance from the camera ray of that pixel to the projection cone, which is the reprojection geometric residual.

[0056] Step S52: Compare the geometric residual with the safety threshold, remove out-of-limit pixels, and obtain a high-fidelity 3D point cloud; Specifically, for each valid pixel, its reprojection geometric residual is compared with a preset safety threshold. This safety threshold is determined based on the calibration accuracy of the measurement system, the image noise level, and the allowable tolerance range of the measured object's surface. It is preset during the system calibration phase. The calibration accuracy includes the statistical value of the residual between the external parameters calibrated between the camera and the projector. The image noise level includes the phase calculation jitter amplitude caused by camera dark field noise and photon shot noise. The tolerance range of the measured object's surface is determined according to the accuracy level of the specific object being measured. Considering these factors, the safety threshold is usually set as a small positive value that matches the measurement accuracy requirements. If the geometric residual is greater than the safety threshold, the pixel is determined to be affected by multipath reflection interference or a phase calculation error, and the corresponding 3D coordinates are considered unreliable, thus the pixel is deleted from the point cloud data. If the geometric residual is less than or equal to the safety threshold, the phase measurement value of the pixel is considered consistent with the spatial geometry, the measurement result is reliable, and the corresponding 3D coordinates are retained. This process is repeated for all valid pixels, performing the above operation pixel by pixel, and all the retained 3D coordinates are aggregated to form the final high-fidelity 3D point cloud data.

[0057] Example 2

[0058] Embodiment 2 of this application provides a three-dimensional measurement system based on multi-step radial structured light and ray conic epipolar geometry, including: The phase-shifting fringe pattern sequence generation module selects topological singularities, calculates the gray level of each pixel through a gray-level distribution function, generates a concentric annular multi-step radial phase-shifting fringe pattern sequence, and projects it sequentially onto the surface of the object being measured. The wrapping phase and modulation acquisition module acquires deformed image sequences and calculates the wrapping phase and modulation per pixel through multi-step phase-shift orthogonal operations. The absolute phase acquisition module uses the topological singularity as the absolute anchor point and the modulation degree as the quality guide. It unwraps the wrapped phase through the region growing space to obtain the absolute phase of the full frame. The 3D coordinate solving module constructs the camera ray and determines the projection cone based on the absolute phase. The 3D coordinates of the measured point are then solved by finding the intersection of the two in spatial geometry. The 3D point cloud acquisition module calculates the spatial geometric residual between the camera ray and the projected cone, removes out-of-limit pixels, and acquires the 3D point cloud.

[0059] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made on the basis of the technical solution of the present invention should be included within the scope of protection of the present invention.

Claims

1. A three-dimensional measurement method based on multi-step radial structured light and ray conic epipolar geometry, characterized in that, include: Step S1: Select topological singularities, calculate the gray level of each pixel through the gray level distribution function, generate a sequence of concentric circular multi-step radial phase-shifting stripe patterns, and project them sequentially onto the surface of the object being measured. Step S2: Acquire the deformed image sequence, and calculate the wrapping phase and modulation degree pixel by pixel through multi-step phase-shifting orthogonal operation; Step S3: Using the topological singularity as the absolute anchor point and the modulation degree as the quality guide, the wrapped phase is unwrapped through the region growing space to obtain the absolute phase of the full frame. Step S4: Construct the camera ray and determine the projection cone surface based on the absolute phase. Solve the three-dimensional coordinates of the measured point by finding the intersection of the two in spatial geometry. Step S5: Calculate the spatial geometric residual between the camera ray and the projection cone, remove out-of-limit pixels, and obtain the 3D point cloud.

2. The three-dimensional measurement method based on multi-step radial structured light and ray conic polar geometry as described in claim 1, characterized in that, Selecting topological singularities, calculating the gray levels of each pixel using a gray-level distribution function, generating a sequence of concentric circular multi-step radial phase-shifting fringe patterns, and projecting them sequentially onto the surface of the object being measured, includes the following sub-steps: Step S11: Select a topological singularity in the projector image plane coordinate system and set the encoding parameters. Calculate the grayscale pixel by pixel with radial Euclidean distance as the independent variable to generate a concentric annular multi-step radial phase-shifting stripe pattern sequence. Step S12: Load the radial phase-shifted stripe pattern sequence onto the projection unit in phase-shift order, and project it onto the surface of the object being measured.

3. The three-dimensional measurement method based on multi-step radial structured light and ray conical epipolar geometry as described in claim 2, characterized in that, The selection of topological singularities includes directly specifying the coordinates of the image plane center, and obtaining sub-pixel-level precise coordinates by projecting a marked pattern and acquiring it by the camera, followed by calibration mapping and back-calculation. The singularity is the geometric center of all concentric ring fringes and the isolated singularity of the phase field.

4. The three-dimensional measurement method based on multi-step radial structured light and ray conical epipolar geometry as described in claim 3, characterized in that, The calibration mapping inverse calculation method involves projecting a crosshair or dot pattern onto a reference plane, extracting the feature point image coordinates after the camera acquires the data, and mapping the feature point coordinates back to the projector image plane coordinate system using the homography matrix obtained through joint calibration of the projector and camera. This inverse calculation yields the sub-pixel level precise coordinates of the topological singularity.

5. The three-dimensional measurement method based on multi-step radial structured light and ray conical epipolar geometry as described in claim 2, characterized in that, The grayscale data of the radial phase-shifted fringe pattern is written into the frame buffer of the projection unit in the phase shift order. The digital micromirror device of the projection unit controls the flipping state of each micromirror according to the grayscale data of each frame. After passing through the illumination source and the projection optical system, the pattern is projected onto the surface of the object being measured.

6. The three-dimensional measurement method based on multi-step radial structured light and ray conical epipolar geometry as described in claim 1, characterized in that, The process involves acquiring a sequence of deformed images, performing multi-step phase-shift orthogonal operations, and calculating the wrapping phase and modulation intensity pixel-by-pixel, including the following sub-steps: Step S21: Sequentially acquire deformed images of each pattern modulated by the surface morphology of the object being measured, to obtain a deformed image sequence; Step S22: Based on the deformed image sequence, calculate the sine and cosine components through multi-step phase-shifting orthogonal operations, and solve the wrapping phase and modulation.

7. The three-dimensional measurement method based on multi-step radial structured light and ray conical epipolar geometry as described in claim 6, characterized in that, A hardware synchronous trigger signal path is established between the projection unit and the image acquisition unit. After the projection unit completes the stable display of each pattern, it sends a trigger signal, and the image acquisition unit performs a synchronous exposure to acquire a frame of deformed image modulated by the surface morphology of the object under test. Patterns are acquired sequentially according to the projection order to obtain a deformed image sequence.

8. The three-dimensional measurement method based on multi-step radial structured light and ray conical epipolar geometry as described in claim 6, characterized in that, Based on deformed image sequences, sinusoidal and cosine components are calculated through multi-step phase-shift orthogonal operations to determine the encapsulation phase and modulation, including the following sub-steps: Step S221: Based on the deformed image sequence, extract the grayscale sequence pixel by pixel, and calculate the sine and cosine components pixel by pixel through multi-step phase-shifting orthogonal operation; Step S222: Calculate the wrapping phase of each pixel based on the sine and cosine components; Step S223: Calculate the modulation index of each pixel based on the sine and cosine components.

9. The three-dimensional measurement method based on multi-step radial structured light and ray conical epipolar geometry as described in claim 1, characterized in that, Calculate the spatial geometric residual between the camera ray and the projected cone, remove out-of-limit pixels, and obtain the 3D point cloud, including the following sub-steps: Step S51: Calculate the spatial geometric residual between the camera ray and the projection cone surface; Step S52: Compare the geometric residual with the safety threshold, remove out-of-limit pixels, and obtain a high-fidelity 3D point cloud.

10. A three-dimensional measurement system based on multi-step radial structured light and ray conic epipolar geometry, characterized in that, include: The phase-shifting fringe pattern sequence generation module selects topological singularities, calculates the gray level of each pixel through a gray-level distribution function, generates a concentric annular multi-step radial phase-shifting fringe pattern sequence, and projects it sequentially onto the surface of the object being measured. The wrapping phase and modulation acquisition module acquires deformed image sequences and calculates the wrapping phase and modulation per pixel through multi-step phase-shift orthogonal operations. The absolute phase acquisition module uses the topological singularity as the absolute anchor point and the modulation degree as the quality guide. It unwraps the wrapped phase through the region growing space to obtain the absolute phase of the full frame. The 3D coordinate solving module constructs the camera ray and determines the projection cone based on the absolute phase. The 3D coordinates of the measured point are then solved by finding the intersection of the two in spatial geometry. The 3D point cloud acquisition module calculates the spatial geometric residual between the camera ray and the projected cone, removes out-of-limit pixels, and acquires the 3D point cloud.

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