A method for measuring the color and uniformity of the surface of supercritical foaming color master batch

Abstract

The application discloses a kind of supercritical foaming color master batch surface global color distribution colorimetry and even dyeing degree characterization method, belong to color measurement and evaluation technical field.This method fixes the color master batch particle to be measured in multi-axis rotary loading platform, and the spectral data and surface height data of multiple visual angle are synchronously collected by line scanning hyperspectral imaging system and line laser triangulation sensor;Fusion generates hyperspectral image cube with height information and calculates surface normal vector;Real spectral radiance is decomposed into diffuse reflection and specular reflection component using spectral radiance correction model, and surface topography interference is eliminated pixel by pixel after nonlinear least squares optimization, and real diffuse reflectance spectrum reflectance is obtained;After conversion into CIE 1976 L*a*b* color space coordinates, the grid covering method is used to calculate the box dimension of color coordinate space distribution;Combined with average color difference, even dyeing degree index is constructed, and the color uniformity of color master batch is comprehensively quantitatively characterized.

Description

Technical Field

[0001] This invention relates to the field of color measurement and evaluation technology, and in particular to a method for measuring the global color distribution and characterizing the uniformity of color on the surface of supercritical foamed color masterbatch. Background Technology

[0002] Supercritical foamed color masterbatch is a functional plastic color masterbatch prepared using supercritical fluid foaming technology. Its surface exhibits a large number of micro- and nano-scale open or closed-cell structures due to the foaming process, resulting in significant three-dimensional undulations. This complex morphology presents unique challenges for color measurement and uniformity evaluation.

[0003] Currently, the primary methods for measuring the color of masterbatches in industry and laboratories are spectrophotometers or colorimeters. These instruments are typically based on integrating spheres or 45° / 0° geometry, with measurement spot diameters ranging from a few millimeters to tens of millimeters, only able to obtain the average spectral reflectance of a localized area of ​​the particle. When there is color inhomogeneity on the masterbatch surface, single-point measurement results are highly random and cannot characterize the global color distribution across the entire particle surface. Even using multi-point measurements and averaging cannot describe the spatial variation of color. More importantly, for rough surfaces like supercritical foamed masterbatches, their microscopic undulations cause incident light to undergo multiple reflections and shadowing at depressions, and generate strong specular reflection components at protrusions, making the measured reflectance spectrum not a true diffuse reflectance spectrum, severely affecting the accuracy of color parameters. The specular reflection traps integrated into conventional instruments are only suitable for macroscopically smooth surfaces and cannot effectively eliminate the complex optical effects introduced by microscopic morphology.

[0004] In imaging-based color measurement, existing techniques mostly employ color or multispectral cameras to photograph planar samples and convert RGB values ​​to the CIE color space based on the assumption of uniform illumination. These methods require the measured surface to be planar and the color texture to be independent of the surface morphology. When applied to particles with three-dimensional morphology, such as supercritical foamed masterbatches, the brightness and hue of each pixel in the image depend not only on the material's own color but also strongly on the local orientation and occlusion state of that point. This results in the directly converted color distribution image containing numerous artifacts, failing to reflect true color differences.

[0005] In evaluating color uniformity, traditional methods heavily rely on manual visual comparison or simple calculations of statistical quantities such as the mean and variance of color difference. These indicators only reflect the average level and dispersion of color deviation, completely ignoring the spatial distribution characteristics of uneven color areas, such as the size, shape, and aggregation degree of color spots. For two masterbatch samples with the same average color difference and variance, one may exhibit fine and uniform textures, while the other may exhibit large color patches. The actual color uniformity effects of the two differ significantly, but traditional indicators cannot distinguish between them. Therefore, there is a lack of a scientific quantitative characterization method that can comprehensively consider both the amount of color deviation and the complexity of color spatial distribution.

[0006] In summary, existing technologies are insufficient to accurately measure the true color of the entire surface of supercritical foamed masterbatch, and lack a means to characterize uniformity of color distribution that can reflect the spatial distribution characteristics of color. Therefore, a new technical solution is urgently needed. Summary of the Invention

[0007] To achieve the above objectives, this invention provides a method for measuring the global color distribution and characterizing the uniformity of color on the surface of supercritical foamed masterbatch, comprising the following steps:

[0008] Step 1: Fix the masterbatch particles to be tested on the multi-axis rotating stage, and adjust the particle position so that the geometric center of the particle is located at the center of the common field of view of the line scanning hyperspectral imaging system and the line laser triangulation sensor. The line scanning hyperspectral imaging system and the line laser triangulation sensor are configured with a coaxial optical path.

[0009] Step 2: Control the multi-axis rotating stage to make the masterbatch particles step at fixed angles along two orthogonal rotation axes, traversing all visible directions of the upper hemisphere of the masterbatch particles to obtain multiple discrete viewpoints. Under each discrete viewpoint, the line-scanning hyperspectral imaging system and the line laser triangulation sensor scan line by line along the latitude direction of the particles. The line-scanning hyperspectral imaging system collects spectral data of multiple spatial pixels on each scanning line, and the line laser triangulation sensor simultaneously collects the height data of the multiple spatial pixels and records the dual-axis angle attitude parameters.

[0010] Step 3: For the data acquired from each discrete viewpoint, the spectral data and height data of each spatial pixel on the same scan line are fused using the spatial mapping relationship between the line scan hyperspectral imaging system and the line laser triangulation sensor to generate a hyperspectral image cube with height information, and the three-dimensional spatial coordinates and surface normal vector of each spatial pixel in the particle reference coordinate system are calculated.

[0011] Step 4: Using the hyperspectral image cube with height information from all discrete viewpoints, establish a spectral radiometric correction model for each spatial pixel. The spectral radiometric correction model represents the measured spectral radiance of the line-scan hyperspectral imaging system as the sum of the diffuse reflection component and the specular reflection component. The diffuse reflection component is proportional to the dot product of the surface normal vector of the spatial pixel and the incident direction vector. The specular reflection component conforms to the Phong illumination model. The true diffuse spectral reflectance is obtained by solving the nonlinear least squares optimization problem.

[0012] Step 5: Convert the true diffuse reflectance obtained in Step 4 into a lightness value in the CIE 1976 L*a*b* color space, combining the CIE standard illuminant D65 relative spectral power distribution and the CIE 1931 standard chromaticity observer spectral tristimulus value function. Color coordinates ;

[0013] Step 6: Perform fractal analysis on the global pixel chromaticity coordinate set obtained in Step 5, and calculate the box-counting dimension of the chromaticity coordinate spatial distribution using the mesh covering method. ;

[0014] Step 7: Determine the reference chromaticity coordinates and reference lightness value, and calculate the color difference for each pixel in the color space. And calculate the arithmetic mean of the color differences of all spatial pixels. ;

[0015] Step 8: Use the box-counting dimension obtained in Step 6 and the arithmetic mean obtained in step 7 Construct the uniformity index U. In the formula This is the space complexity weighting coefficient.

[0016] Preferably, the step angle of the fixed angle stepping in step 2 is a fixed value between 5° and 15°; the multi-axis rotating stage has two orthogonal rotational degrees of freedom, the rotational angular displacement resolution of the multi-axis rotating stage is not less than 0.1°, and the coincidence deviation between the rotation center of the multi-axis rotating stage and the center of the common field of view is less than 0.05 mm; the traversal of all visible directions of the upper hemisphere of the masterbatch particles specifically involves: first, making the multi-axis rotating stage step around the first rotation axis at the fixed angle, and after each stepping around the first rotation axis, then stepping around the second rotation axis at the fixed angle to complete one full revolution, thereby obtaining M discrete viewing angles.

[0017] Preferably, in step 2, the wavelength range of the spectral data acquired by the line-scan hyperspectral imaging system is 400 nm to 700 nm, the spectral sampling interval is 10 nm, and the number of spatial pixels on each scan line is N, where N ≥ 200; the height measurement accuracy of the line laser triangulation sensor is better than 2 μm; and the line-scan hyperspectral imaging system and the line laser triangulation sensor acquire data synchronously with the same scanning rhythm.

[0018] Preferably, the calculation of the surface normal vector of each spatial pixel in step 3 specifically involves: performing least-squares plane fitting on the height data of each spatial pixel in its local neighborhood, and using the unit normal vector of the fitted plane as the surface normal vector of the corresponding spatial pixel; each spatial pixel in the hyperspectral image cube with height information records a set of spectral radiance vectors and a scalar height value; the three-dimensional spatial coordinates are calculated based on the dual-axis angle attitude parameters and imaging geometry.

[0019] Preferably, the spectral radiometric correction model described in step 4 is for the measured spectral radiance of the i-th spatial pixel at the j-th viewpoint. satisfy:

[0020]

[0021] In the formula, Let be the true diffuse spectral reflectance of the i-th spatial pixel. Let i be the surface unit normal vector of the i-th spatial pixel. Let be the unit direction vector of the incident light from the j-th viewpoint. Let be the specular reflection intensity coefficient of the i-th spatial pixel. Let be the specular reflection direction vector of the incident light with respect to the unit normal vector of the surface. Let be the observation direction vector of the j-th viewpoint. The specular reflection sharpness index. The value range is from 10 to 100.

[0022] Preferably, in step 4, the nonlinear least squares optimization solution employs the Levenberg-Marquardt algorithm, aiming to minimize the sum of squared residuals between the model-calculated values ​​and the measured spectral radiance at each wavelength under all discrete viewpoints, and iteratively optimizes the solution for each spatial pixel. and And during the solution process, Apply a smoothness constraint in the wavelength dimension.

[0023] Preferably, the box-counting dimension of the chromaticity coordinate space distribution calculated using the grid covering method in step 6 is... Specifically, in a two-dimensional chromaticity plane, a series of square grids with side lengths are selected. The side lengths are taken as 2, 3, 4, 6, 8, 12, 16, 24, and 32 CIELAB chroma units respectively. For each side length... Count the number of grids that can cover at least one spatial pixel chromaticity coordinate projection point. In a double logarithmic coordinate system, with The x-axis is... Scatter points were plotted on the ordinate, and a least-squares straight line was fitted. The slope of the resulting line was used as the box-counting dimension. .

[0024] Preferably, determining the reference chromaticity coordinates in step 7 specifically involves: performing two-dimensional kernel density estimation on the global spatial pixel chromaticity coordinate set obtained in step 5, using a Gaussian kernel function with bandwidth automatically determined according to the Scott criterion; calculating the probability density of each point on the chromaticity plane; and taking the chromaticity coordinates corresponding to the point with the maximum probability density as the reference chromaticity coordinates. The reference brightness value is the median of the brightness values ​​of all spatial pixels.

[0025] Preferably, the space complexity weighting coefficient in step 8 The value ranges from 0.5 to 2.0.

[0026] Preferably, the conversion to lightness values ​​in step 5 refers to the conversion to the CIE 1976 L*a*b* color space. Color coordinates Specifically, this includes: for the i-th spatial pixel, based on the true diffuse reflectance spectrum... CIE standard illuminant D65 relative spectral power distribution and the CIE 1931 standard colorimetric observer spectral tristimulus value function Calculate the CIE XYZ tristimulus values:

[0027]

[0028]

[0029]

[0030] Where the normalization coefficient , The wavelength sampling interval is defined; then, according to the CIE 1976 L*a*b*chromatic difference formula, the wavelength sampling interval is determined. Convert to lightness value Color coordinates .

[0031] The beneficial effects of this invention are:

[0032] 1. This invention establishes a spectral radiometric correction model for each spatial pixel by coaxially and synchronously acquiring data through multi-view line-scan hyperspectral imaging and a line laser triangulation sensor. This model explicitly decomposes the measured spectral radiance into a diffuse reflection component proportional to the dot product of the surface normal vector and the incident direction, and a specular reflection component conforming to the Phong illumination model. The true diffuse spectral reflectance is solved pixel by pixel through Levenberg-Marquardt nonlinear least squares optimization combined with spectral smoothing constraints. This physically eliminates the interference of shadow occlusion and specular reflection highlights caused by micro-undulations on the surface of supercritical foamed masterbatch on color measurement, making the color measurement results reflect the inherent color properties of the material rather than morphology artifacts. This significantly improves the accuracy and repeatability of color measurement on complex morphological surfaces.

[0033] 2. This invention introduces fractal box-counting dimension into the evaluation of color uniformity of masterbatch for the first time. By performing fractal analysis on the grid coverage of global pixel chromaticity coordinates on a two-dimensional chromaticity plane, the box-counting dimension of chromaticity spatial distribution is quantitatively obtained. This dimension quantifies the dispersion degree of color-uniform spots and self-similar texture structure characteristics in the color space, making up for the fundamental defect of traditional uniformity evaluation that only relies on average color difference or color difference variance and completely ignores the color space distribution pattern. This allows samples with different spatial distribution patterns but similar average color differences to be effectively distinguished.

[0034] 3. The uniformity index constructed in this invention organically integrates the average color difference with the box dimension of the chromaticity space. By adjusting the weighting coefficient of spatial complexity, it can flexibly balance the contribution of color deviation amplitude and color space distribution complexity to the evaluation of uniformity according to actual application needs. This index unifies the degree of color deviation and the distribution complexity of color spots into a dimensionless quantitative indicator, realizing a comprehensive, objective and highly discriminative characterization of the uniformity of supercritical foaming masterbatch, and providing a scientific quantitative basis for industrial quality control. Attached Figure Description

[0035] To more clearly illustrate the technical solutions in this 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 for this invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0036] Figure 1 This is a flowchart of the steps of the method of the present invention. Detailed Implementation

[0037] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. It should also be noted that, to make the embodiments more comprehensive, the following embodiments are the best and preferred embodiments, and those skilled in the art can use other alternative methods to implement some well-known technologies; moreover, the accompanying drawings are only for more specific description of the embodiments and are not intended to specifically limit the present invention.

[0038] Please see Figure 1 This invention provides a method for measuring the global color distribution and characterizing the uniformity of color on the surface of supercritical foamed color masterbatch. This method combines multi-view line-scanning hyperspectral imaging with line laser triangulation to simultaneously acquire topography. By establishing a photometric correction framework that includes surface normal vectors and a Phong specular reflection model, the interference of microscopic undulations on the particle surface on color measurement is eliminated, and the true diffuse reflectance of all spatial pixels on the particle surface is obtained. On this basis, the spatial texture features of color non-uniformity are quantified using the fractal box dimension of chromaticity space, and a uniformity index is constructed in conjunction with the average color difference, thereby achieving a scientific quantitative characterization of the color uniformity of the color masterbatch.

[0039] It is understandable that:

[0040] Regarding the multi-axis rotating stage and coaxial optical path configuration in step 1: The multi-axis rotating stage has at least two orthogonal rotational degrees of freedom, a first rotational axis and a second rotational axis. The first rotational axis is arranged horizontally, and the second rotational axis is arranged vertically, intersecting at the stage's rotation center. The stage's rotational angular displacement resolution is no less than 0.1° to ensure precise stepping. The particle position is adjusted so that the particle's geometric center is located at the center of the common field of view of the line-scan hyperspectral imaging system and the line laser triangulation sensor. The overlap deviation between the stage's rotation center and the common field of view center must be less than 0.05 mm, which is achieved through mechanical adjustment and calibration. The coaxial optical path configuration of the line-scan hyperspectral imaging system and the line laser triangulation sensor means that the main optical axis of the line-scan hyperspectral imaging system and the optical axis of the laser beam emitted by the line laser triangulation sensor are merged into the same optical axis through a beam-splitting prism. This ensures that during a single line scan, the spatial pixel corresponding to a scan line acquired by the hyperspectral system corresponds precisely to the height sampling point of the same scan line acquired by the triangulation sensor, achieving pixel-level spatial synchronization of spectral data and height data.

[0041] Regarding step 2, which involves traversing all visible directions of the upper hemisphere, the fixed angle step value is selected between 5° and 15°, for example, 10°. The traversal process is as follows: First, place the first rotation axis at the initial angle position, then rotate the second rotation axis at equal intervals of the step angle, recording one frame of data at each step; subsequently, the first rotation axis steps by a fixed angle, and the second rotation axis rotates again to collect data; this cycle continues until the cumulative rotation angle of the first rotation axis covers the required range of the upper hemisphere of the particle. For upper hemisphere coverage, the angle range of the first rotation axis is generally 0° to 180° (or -90° to +90°), specifically determined according to the stage structure. The total number of discrete viewing angles M obtained depends on the step angle. For example, with a step of 10°, the first rotation axis has 19 positions (0° to 180°), and the second rotation axis has 36 viewing angles at each position, for a total of 684 viewing angles. At each discrete viewpoint, the spectral data wavelength range of the line-scan hyperspectral imaging system is 400 nm to 700 nm, with a spectral sampling interval of 10 nm, resulting in a total of 31 spectral channels. The number of spatial pixels N on each scan line is set according to the system magnification and particle size, with N not less than 200, typically 256 or 512. The height data from the line laser triangulation sensor is synchronized with the spectral data, achieving a height measurement accuracy better than 2 micrometers.

[0042] Regarding the surface normal vector calculation in step 3: The surface normal vector is obtained by performing least-squares plane fitting on the height data within the local neighborhood of each spatial pixel. Specifically: for the i-th spatial pixel, take the height data centered on it... The height data within the window, with a side length w of 5 or 7 pixels, is used to fit the plane equation z = ax + by + c. The coefficients a, b, and c are solved using the least squares method. The unit normal vector of this plane is then obtained.

[0043]

[0044] This unit normal vector is represented in the particle reference coordinate system. The particle reference coordinate system has its origin at the geometric center of the particle, and its Z-axis coincides with the second rotation axis of the stage.

[0045] Regarding the spectral radiance correction model in step 4, this model is a core technical means to eliminate morphological interference and obtain true color. The physical basis of the model is that the spectral radiance received by the sensor comes from two parts: diffuse reflection of the material itself and specular reflection of the surface. The diffuse reflection part follows Lambert's cosine law, and its intensity is proportional to the dot product of the surface normal vector and the incident light direction vector; the specular reflection part is not negligible on smooth or semi-smooth surfaces and is described by the Phong illumination model, that is, the specular reflection intensity decreases with a power of the cosine of the angle between the observation direction and the specular reflection direction. For the i-th spatial pixel at the j-th viewpoint, the measured spectral radiance is... The relationship with each geometric parameter is as follows:

[0046]

[0047] In the formula, The incident light unit direction vector is determined by the position of the illumination device. In the coaxial optical path configuration of the present invention, the incident light direction is consistent with or nearly consistent with the observation direction. However, when the illumination and observation are not coaxial, this vector needs to be precisely calibrated. For incident light about The specular reflection direction vector is calculated using the following formula: . Let be the unit vector of the observation direction at the j-th viewpoint, pointing to the center of the entrance pupil of the line-scan hyperspectral imaging system. The specular reflection sharpness index controls the convergence and divergence of highlights, with a value ranging from 10 to 100; for foamed surfaces with high roughness, A smaller value is preferable, such as 20; for smoother resin surfaces, A larger value can be taken, such as 60. In nonlinear least squares optimization, the Levenberg-Marquardt algorithm is used, and the objective function is:

[0048]

[0049] To ensure solution stability and suppress spectral dimensional noise, diffuse reflectance spectra are processed. Apply a smoothness constraint along the wavelength dimension, i.e., add a Tikhonov regularization term to the objective function, so that the smoothness at adjacent wavelengths is achieved. The value changes gradually. The regularization parameter is determined using the L-curve method. After optimization, the output of each spatial pixel is... This is the true diffuse reflectance spectrum after removing geometric factors.

[0050] Regarding the color space conversion in step 5, first calculate the XYZ tristimulus values ​​of the i-th pixel according to the CIE standard formula:

[0051]

[0052]

[0053]

[0054] The wavelength summation is performed in 10-nanometer increments, resulting in 31 terms. The relative spectral power distribution of the D65 illuminator. Let be the tristimulus value function of the spectral spectrum for the CIE 1931 2° standard colorimetric observer, and k be the normalization coefficient. The CIE1976 L*a*b* coordinate transformation formula is as follows:

[0055]

[0056]

[0057]

[0058] in Let f(t) be the reference white tristimulus value of the D65 illuminator at a 2° field of view. The function f(t) is defined as: when hour, Otherwise, f(t) = (841 / 108)t + 16 / 116.

[0059] Regarding the fractal box dimension calculation in step 6. In a two-dimensional plane, the set of chromatic coordinates of pixels constitutes a point set. The mesh covering method is used to calculate the box-dimensionality. The process is as follows: Select a series of grid side lengths The set of possible values ​​is selected by this method. The unit is CIELAB chromaticity units. For each ,Will The plane has a side length of Divide the grid into square grids and count the number of grids containing at least one chromaticity projection point. Then, a least-squares linear fit was performed. about The scatter plot has a slope of . The box dimension characterizes the complexity of the distribution of color points in chromaticity space and their ability to fill the space. The more concentrated the distribution, the more complex the distribution. The smaller the size, the more diffuse the distribution and the more self-similar the structure. The larger.

[0060] Regarding the determination of reference chromaticity coordinates in step 7: To objectively represent the main color of the masterbatch, a two-dimensional kernel density estimation method is used to find the chromaticity coordinates where the color distribution is most concentrated. The kernel density estimation formula is:

[0061]

[0062] in Here, h represents the standard Gaussian kernel function, and h is the bandwidth. The bandwidth is automatically calculated using the Scott criterion. Where d=2 is the dimension. This represents the geometric mean of the standard deviations for each dimension. Dense sampling on a plane calculates the probability density; the point with the highest density corresponds to... Used as a reference chromaticity coordinate. Reference lightness value. The median of all pixel brightness values ​​is used to avoid the influence of extremely bright or dark pixels. Then, the color difference of each pixel is calculated, and finally, the arithmetic mean of the color differences of all pixels is taken. .

[0063] Regarding the construction of the uniformity index in step 8: The uniformity index U combines the average color difference and the box dimension.

[0064]

[0065] Space complexity weight coefficient The value ranges from 0.5 to 2.0 and can be set according to application requirements. Taking 1.0 as a balance point, the color space distribution complexity and average color difference have equal weight in influencing the uniformity of color. If the application focuses more on the regularity of color patch texture, the value can be increased. Value; if more attention is paid to the absolute magnitude of color deviation, it can be reduced. The higher the U-value, the better the uniformity of color. This index has good discriminative power and can effectively distinguish samples with similar average color differences but drastically different spatial distributions of color spots.

[0066] The technical solution of the present invention will be further described below with reference to specific embodiments.

[0067] Example

[0068] The sample tested in this embodiment is a blue supercritical foaming masterbatch particle. The particle is approximately spherical with a diameter of about 3.5 mm and has a micron-sized open-pore foaming structure on its surface.

[0069] Step 1: Fix the masterbatch particles to be tested onto a multi-axis rotating stage. The stage has an orthogonal first rotation axis (horizontal) and a second rotation axis (vertical), with a rotational angular displacement resolution of 0.05°. The deviation between the rotation center and the common field of view center is calibrated to 0.03 mm using a laser interferometer. The line-scan hyperspectral imaging system operates in the 400 nm to 700 nm wavelength band, with a spectral sampling interval of 10 nm and a spatial pixel count set to N=256. The line laser triangulation sensor has a height measurement accuracy of 1.5 μm and shares a coaxial optical path with the hyperspectral system.

[0070] Step 2: Set the fixed step angle to 10°. First, set the first rotation axis to 0°. Then, start the second rotation axis from 0° and rotate 360° in 10° steps, for a total of 36 angular positions. At each position, simultaneously acquire one frame of spectral data and altitude data. Then, the first rotation axis steps 10° to 10°, and the second rotation axis completes the acquisition at another 36 positions. Repeat this process until the first rotation axis reaches 180°, obtaining a total of [data missing]. Data from discrete viewpoints. At each viewpoint, the line-scan hyperspectral imaging system scans along the latitudinal direction of the particle, obtaining the spectral radiance of N=256 spatial pixels, with each spatial pixel corresponding to 31 wavelength channels; a line laser triangulation sensor simultaneously acquires 256 height values. The dual-axis angular attitude parameters corresponding to each viewpoint are recorded. .

[0071] Step 3: Utilizing the pre-calibrated spatial mapping relationship, the spectral data and height data from each viewpoint are fused pixel-level to generate 684 hyperspectral image cubes with height information. Each image cube contains 256 pixels, and each pixel records 31-dimensional spectral radiance and one height value. Based on the angle and attitude parameters and imaging geometry, the pixel coordinates are transformed to the particle reference coordinate system to obtain the three-dimensional spatial coordinates of each pixel. A window with w=5 is used to perform least-squares plane fitting on the local neighborhood height data of each pixel to calculate the surface unit normal vector. .

[0072] Step 4: For the blue foamed masterbatch in this embodiment, the specular reflection sharpness index is preferably selected based on previous experiments. Incident light direction and observation direction Based on the system's geometric calibration data, in this system and Basically parallel. The Levenberg-Marquardt algorithm is used to optimize the solution for each pixel. and The spectral smoothing regularization parameter was set to 0.01. After approximately 120 seconds of calculation, the true diffuse spectral reflectance of all 256×684 spatial pixels was obtained. .

[0073] Step 5: Using the D65 standard illuminator and the 2° standard observer function, calculate the XYZ values ​​for each pixel, and then convert them to... Values. Examples of partial pixel color data are shown below (only 3 representative points are listed):

[0074] Pixels , ,

[0075] Pixels , ,

[0076] Pixels , ,

[0077] Step 6: Set of chromaticity coordinates for all pixels in the global domain Box dimension calculation was performed using the mesh covering method. The selected method... The sequence is 2, 3, 4, 6, 8, 12, 16, 24, 32. The statistical results are shown in Table 1.

[0078] Table 1 Different grid side lengths Number of coverage grids below

[0079]

[0080] right and Linear fitting yields the slope. .

[0081] Step 7: Through two-dimensional kernel density estimation, the bandwidth of the Gaussian kernel function is determined by the Scott criterion to be h = 1.53 CIELAB units. The reference chromaticity coordinates corresponding to the point of maximum probability density are... , The median value is used as the reference brightness value. Calculate the color difference of each pixel to obtain the average color difference. .

[0082] Step 8: Obtain the space complexity weighting coefficient Calculate the uniformity index:

[0083]

[0084] To demonstrate the effectiveness of the method in this embodiment, a comparative experiment was conducted. The comparative experiment used a conventional single-point integrating sphere spectrophotometer (geometric condition d / 8°) to perform six random position measurements on the same masterbatch, and the average color difference of the six measurements was calculated (using the average of the six measurements as a reference). The average color difference measured by the comparative method was... However, this method cannot obtain chromaticity spatial distribution information, and therefore cannot calculate the box dimension and uniform chromaticity index. For a more comprehensive comparison, the chromaticity coordinates obtained by the method in this embodiment are directly used to calculate the traditional standard deviation of color difference, resulting in... Further comparison with a substandard masterbatch exhibiting obvious blocky and uneven coloring revealed that this method measured... , The result was U=0.127; while the traditional method only yielded an average color difference of 2.95, failing to distinguish differences in uniformity. The comparison results are shown in Table 2.

[0085] Table 2 Comparison of results between the method in this embodiment and the comparative method.

[0086]

[0087] As can be seen from the table above, the traditional method, based solely on the average color difference, shows a difference of 0.64 between defective and normal products. However, this method, in addition to the difference in average color difference, also reveals a more complex spatial distribution of color spots in defective products. (From 1.28 to 1.52), the overall uniformity index decreased from 0.154 to 0.127, and the discrimination was significantly better than that of simple average color difference comparison.

[0088] The above embodiments demonstrate that the method of the present invention can effectively eliminate the surface morphology interference of supercritical foaming masterbatch, obtain the true color distribution of the entire domain, and realize a comprehensive evaluation including spatial characteristics through the uniformity index.

[0089] This invention encompasses any substitutions, modifications, equivalent methods, and solutions made within the spirit and scope of this invention. To provide the public with a thorough understanding of this invention, specific details are described in detail in the following preferred embodiments; however, those skilled in the art will fully understand the invention even without these details. Furthermore, to avoid unnecessary misunderstanding of the essence of this invention, well-known methods, processes, procedures, components, and circuits are not described in detail.

[0090] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for measuring the global color distribution and characterizing the uniformity of color on the surface of supercritical foamed masterbatch, characterized in that, Includes the following steps: Step 1: Fix the masterbatch particles to be tested on the multi-axis rotating stage, and adjust the particle position so that the geometric center of the particle is located at the center of the common field of view of the line scanning hyperspectral imaging system and the line laser triangulation sensor. The line scanning hyperspectral imaging system and the line laser triangulation sensor are configured with a coaxial optical path. Step 2: Control the multi-axis rotating stage to make the masterbatch particles step at fixed angles along two orthogonal rotation axes, traversing all visible directions of the upper hemisphere of the masterbatch particles to obtain multiple discrete viewpoints. Under each discrete viewpoint, the line-scanning hyperspectral imaging system and the line laser triangulation sensor scan line by line along the latitude direction of the particles. The line-scanning hyperspectral imaging system collects spectral data of multiple spatial pixels on each scanning line, and the line laser triangulation sensor simultaneously collects the height data of the multiple spatial pixels and records the dual-axis angle attitude parameters. Step 3: For the data acquired from each discrete viewpoint, the spectral data and height data of each spatial pixel on the same scan line are fused using the spatial mapping relationship between the line scan hyperspectral imaging system and the line laser triangulation sensor to generate a hyperspectral image cube with height information, and the three-dimensional spatial coordinates and surface normal vector of each spatial pixel in the particle reference coordinate system are calculated. Step 4: Using the hyperspectral image cube with height information from all discrete viewpoints, establish a spectral radiometric correction model for each spatial pixel. The spectral radiometric correction model represents the measured spectral radiance of the line-scan hyperspectral imaging system as the sum of the diffuse reflection component and the specular reflection component. The diffuse reflection component is proportional to the dot product of the surface normal vector of the spatial pixel and the incident direction vector. The specular reflection component conforms to the Phong illumination model. The true diffuse spectral reflectance is obtained by solving the nonlinear least squares optimization problem. Step 5: Convert the true diffuse reflectance obtained in Step 4 into a lightness value in the CIE 1976 L*a*b* color space by combining the CIE standard illuminant D65 relative spectral power distribution and the CIE 1931 standard chromaticity observer spectral tristimulus value function. Color coordinates ; Step 6: Perform fractal analysis on the global pixel chromaticity coordinate set obtained in Step 5, and calculate the box-counting dimension of the chromaticity coordinate spatial distribution using the mesh covering method. ; Step 7: Determine the reference chromaticity coordinates and reference lightness value, and calculate the color difference for each pixel in the color space. And calculate the arithmetic mean of the color differences of all spatial pixels. ; Step 8: Use the box-counting dimension obtained in Step 6 and the arithmetic mean obtained in step 7 Construct the uniformity index U. In the formula This is the space complexity weighting coefficient.

2. The method for measuring the global color distribution and characterizing the uniformity of color on the surface of supercritical foamed masterbatch according to claim 1, characterized in that, In step 2, the step angle of the fixed angle stepping is a fixed value between 5° and 15°; the multi-axis rotating stage has two orthogonal rotational degrees of freedom, the rotational angular displacement resolution of the multi-axis rotating stage is not less than 0.1°, and the coincidence deviation between the rotation center of the multi-axis rotating stage and the center of the common field of view is less than 0.05 mm; the traversal of all visible directions on the upper hemisphere of the masterbatch particles is specifically as follows: first, the multi-axis rotating stage steps around the first rotation axis at the fixed angle, and after each stepping around the first rotation axis, it steps around the second rotation axis at the fixed angle to complete one full revolution, thereby obtaining M discrete viewing angles.

3. The method for measuring the global color distribution and characterizing the uniformity of color on the surface of supercritical foamed masterbatch according to claim 1, characterized in that, The wavelength range of the spectral data acquired by the line-scanning hyperspectral imaging system in step 2 is 400 nm to 700 nm, the spectral sampling interval is 10 nm, and the number of spatial pixels on each scan line is N, where N ≥ 200; the height measurement accuracy of the line laser triangulation sensor is better than 2 μm; the line-scanning hyperspectral imaging system and the line laser triangulation sensor acquire data synchronously with the same scanning rhythm.

4. The method for measuring the global color distribution and characterizing the uniformity of color on the surface of supercritical foamed masterbatch according to claim 1, characterized in that, Step 3, which involves calculating the surface normal vector of each spatial pixel, specifically involves: performing least-squares plane fitting on the height data of each spatial pixel in its local neighborhood, and using the unit normal vector of the fitted plane as the surface normal vector of the corresponding spatial pixel; each spatial pixel in the hyperspectral image cube with height information records a set of spectral radiance vectors and a scalar height value; the three-dimensional spatial coordinates are calculated based on the dual-axis angle pose parameters and imaging geometry.

5. The method for measuring the global color distribution and characterizing the uniformity of color on the surface of supercritical foamed masterbatch according to claim 1, characterized in that, The spectral radiometric correction model described in step 4 is for the measured spectral radiance of the i-th spatial pixel at the j-th viewpoint. satisfy: In the formula, Let be the true diffuse spectral reflectance of the i-th spatial pixel. Let i be the surface unit normal vector of the i-th spatial pixel. Let be the unit direction vector of the incident light from the j-th viewpoint. Let be the specular reflection intensity coefficient of the i-th spatial pixel. Let be the specular reflection direction vector of the incident light with respect to the unit normal vector of the surface. Let be the observation direction vector of the j-th viewpoint. The specular reflection sharpness index. The value range is from 10 to 100.

6. The method for measuring the global color distribution and characterizing the uniformity of color on the surface of supercritical foamed masterbatch according to claim 5, characterized in that, Step 4 describes a nonlinear least squares optimization solution using the Levenberg-Marquardt algorithm. The objective is to minimize the sum of squared residuals between the calculated model values ​​and the measured spectral radiance at each wavelength across all discrete viewpoints. This is achieved through iterative optimization for each spatial pixel. and And during the solution process, Apply a smoothness constraint in the wavelength dimension.

7. The method for measuring the global color distribution and characterizing the uniformity of color on the surface of supercritical foamed masterbatch according to claim 1, characterized in that, Step 6 describes using the grid covering method to calculate the box-count dimension of the chromaticity coordinate space distribution. Specifically, in a two-dimensional chromaticity plane, a series of square grids with side lengths are selected. The side lengths are taken as 2, 3, 4, 6, 8, 12, 16, 24, and 32 CIELAB chroma units respectively. For each side length... Count the number of grids that can cover at least one spatial pixel chromaticity coordinate projection point. In a double logarithmic coordinate system, with The x-axis is... Scatter points were plotted on the ordinate, and a least-squares straight line was fitted. The slope of the resulting line was used as the box-counting dimension. .

8. The method for measuring the global color distribution and characterizing the uniformity of color on the surface of supercritical foamed masterbatch according to claim 1, characterized in that, Step 7, determining the reference chromaticity coordinates, specifically involves: performing two-dimensional kernel density estimation on the global pixel chromaticity coordinate set obtained in step 5, using a Gaussian kernel function with bandwidth automatically determined according to the Scott criterion; calculating the probability density of each point on the chromaticity plane; and taking the chromaticity coordinates corresponding to the point with the maximum probability density as the reference chromaticity coordinates. The reference brightness value is the median of the brightness values ​​of all spatial pixels.

9. The method for measuring the global color distribution and characterizing the uniformity of color on the surface of supercritical foamed masterbatch according to claim 1, characterized in that, The space complexity weighting coefficient mentioned in step 8 The value range is from 0.5 to 2.

0.

10. The method for measuring the global color distribution and characterizing the uniformity of color on the surface of supercritical foamed masterbatch according to claim 1, characterized in that, The conversion to lightness values ​​in step 5, as described, is for the CIE 1976 L*a*b* color space. Color coordinates Specifically, this includes: for the i-th spatial pixel, based on the true diffuse reflectance spectrum... CIE standard illuminant D65 relative spectral power distribution and the CIE 1931 standard colorimetric observer spectral tristimulus value function Calculate the CIE XYZ tristimulus values: Where the normalization coefficient , The wavelength sampling interval is defined; then, according to the CIE 1976 L*a*b*chromatic difference formula, the wavelength sampling interval is determined. Convert to lightness value Color coordinates .

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