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CN119540500B - Multi-surface reflection error correction method and equipment for pressure-sensitive paint measurement - Google Patents

Multi-surface reflection error correction method and equipment for pressure-sensitive paint measurement

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Publication number
CN119540500B
CN119540500B CN202411632622.6A CN202411632622A CN119540500B CN 119540500 B CN119540500 B CN 119540500B CN 202411632622 A CN202411632622 A CN 202411632622A CN 119540500 B CN119540500 B CN 119540500B
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pressure
image
surface reflection
camera
sensitive paint
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CN119540500A (en
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朱自超
彭迪
刘应征
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Shanghai Jiao Tong University
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    • G—PHYSICS
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    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T19/00—Manipulating 3D models or images for computer graphics
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N21/00—Investigating or analysing materials by the use of optical means, i.e. using sub-millimetre waves, infrared, visible or ultraviolet light
    • G01N21/17—Systems in which incident light is modified in accordance with the properties of the material investigated
    • G01N21/47—Scattering, i.e. diffuse reflection
    • G—PHYSICS
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    • G01N21/47—Scattering, i.e. diffuse reflection
    • G01N21/4738—Diffuse reflection, e.g. also for testing fluids, fibrous materials
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Abstract

The invention relates to a multi-surface reflection error correction method and equipment for pressure-sensitive paint measurement, which introduces a micro-optical line tracking technology to simulate the process from 'pressure-sensitive paint luminescence to camera imaging', and accurately analyzes the real luminescence intensity of the pressure-sensitive paint on the surface of a model through a counter-propagation algorithm based on known parameters such as the reflectivity of the pressure-sensitive paint, the resolution of an image, the relative position of a camera and the model placement and the like. Finally, by adjusting the reflection parameters of the pressure-sensitive paint to zero, an image without reflection influence under the imaging visual angle of the camera is directly generated, so that the corresponding relation between the image pixel points and the model surface is maintained unchanged while the multi-surface reflection interference is effectively eliminated, and an additional image registration step is avoided. Compared with the prior art, the invention has the advantages of high measurement precision, wide application scene, low cost and the like.

Description

Multi-surface reflection error correction method and equipment for pressure-sensitive paint measurement
Technical Field
The invention relates to the technical field of aerodynamic and hydrodynamic testing, in particular to a multi-surface reflection error correction method and equipment for pressure-sensitive paint measurement.
Background
Pressure sensitive paint (Pressure SENSITIVE PAINT, PSP) is an advanced optical measurement technology, and by spraying special paint on the surface of a model and utilizing UV light source excitation, the Pressure change of the surface of the model to be measured is measured by utilizing the oxygen quenching effect in the photoluminescence process. Compared with the traditional contact pressure measuring method, the technology has the advantages of high spatial resolution, low cost, good model adaptability and the like, and has been widely applied to aerodynamic experiments.
The problem of PSP emissions reflecting each other at adjacent surfaces is likely to occur at corner locations of the model (e.g., where the wing joins the fuselage). The images of such clutter will not be removed by image contrast or in situ calibration in areas where the pressure gradient is highly variable, which will seriously affect the measurement accuracy of the PSP technique. Therefore, it is highly desirable to perform error correction on such images with multiple surface reflection problems, so as to obtain a real optical signal of the surface to be measured, and realize high-precision measurement of the PSP.
The error correction method of multi-surface reflection widely adopted at present is mainly based on calculation of a large linear equation set, and has high requirements on the number and curvature change of three-dimensional triangular grids, the corresponding relation between the three-dimensional grids and two-dimensional images and the like. In addition, since the two-dimensional pixel points and the three-dimensional triangular patches are not in one-to-one correspondence, a large amount of interpolation and approximation are required in the correction process. Therefore, the existing method has higher calculation cost and more practical application limit, and can not realize the accurate and reliable correction of the multi-surface reflection errors of the pressure-sensitive coating.
In summary, there is currently a lack of a multi-surface reflection error correction method to solve or partially solve the foregoing problems.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provide a multi-surface reflection error correction method and equipment for pressure-sensitive paint measurement so as to realize accurate and reliable correction of the multi-surface reflection error of the pressure-sensitive paint.
The aim of the invention can be achieved by the following technical scheme:
in one aspect of the present invention, a method for correcting multi-surface reflection errors for pressure sensitive paint measurement is provided, comprising the steps of:
acquiring the reflectivity of the pressure-sensitive coating at the wavelength of emitted light;
Acquiring triangular mesh data of a region to be tested on multiple surfaces;
Acquiring a real luminous image of the region to be tested of the multiple surfaces sprayed with the pressure sensitive paint, and camera parameters when the real luminous image is shot;
initializing luminous intensity of each triangular patch in the region to be detected based on the triangular mesh data and the camera parameters, acquiring a simulation image of the region to be detected with multiple surfaces corresponding to the reflectivity of the emitted light wavelength through micro-optical line tracking, and performing iterative optimization on the simulation image with the aim of minimizing simulation errors between the simulation image and the real luminous image;
and (3) configuring the reflectivity of the pressure-sensitive paint to be zero based on the simulated image after iterative optimization, and acquiring a corrected image with zero surface reflection through microlithography tracking.
As a preferred technical scheme, the calculation process of the simulation error comprises the following steps:
And capturing difference information of the simulation image and the real luminous image under different scales through multi-scale Gaussian filtering and downsampling, and calculating simulation errors.
As a preferred technical solution, the simulation error is calculated by the following formula:
Wherein img_1 is a real luminous image, img_2 n represents a simulation image obtained by using a microlithography tracking technology in the nth iteration, diff represents a difference image under different scales, avgPool 2×2 is an average pooling layer with the size of 2×2, gf 7×7 is a gaussian filter kernel with the size of 7×7, uniform zero filling is performed on the image boundary in the filtering process, padding is a filling value, h and w represent the high and wide pixel numbers of an original image respectively, and loss is an analog error.
As a preferred technical solution, in the iterative optimization process, the light intensity of each pixel point is updated by adopting the following formula:
I=∫∫f(u,v;C,E)dudv
wherein I is light intensity information of the pixel point, f is a scene function including camera, model and light source parameters, C, E is camera parameters and luminous intensity of each triangular patch respectively.
As a preferable technical scheme, when the simulation error is smaller than a preset threshold value or the iteration number exceeds a set value, the iterative optimization is terminated.
As a preferred embodiment, the camera parameters include an image resolution, a camera position, a camera orientation, a camera field angle, and a height direction in which the camera captures an image.
As a preferable technical scheme, the sizes of the triangular patches on the multiple surfaces are configured, so that each triangular patch can reflect the luminous intensity of the corresponding area.
As a preferable technical scheme, the measuring process of the reflectivity of the wavelength of the emitted light comprises the following steps:
The reflectance of the pressure sensitive paint at the emitted light band was measured using an integrating sphere.
In another aspect of the invention, an electronic device is provided that includes one or more processors and memory having stored therein one or more programs including instructions for performing the aforementioned method of multi-surface reflection error correction for pressure sensitive paint measurement.
In another aspect of the invention, a computer-readable storage medium is provided that includes one or more programs for execution by one or more processors of an electronic device, the one or more programs including instructions for performing the aforementioned method of multi-surface reflection error correction for pressure-sensitive paint-facing measurements.
Compared with the prior art, the invention has at least one of the following beneficial effects:
(1) The invention overcomes the defects of large calculated amount and more model limitation in the prior art, obviously improves the final measurement accuracy through a refined error correction flow, has simple and practical whole correction process, wide applicability, can effectively cope with the multi-surface reflection challenges of various complex models based on pressure-sensitive paint measurement, and provides powerful support for realizing the measurement of the pressure-sensitive paint with high accuracy and high reliability.
(2) The method has the advantages of wide application scene and low cost, only needs to ensure the size and reconstruction precision of the three-dimensional triangular mesh of the model to be detected, has no additional limitation on factors such as the change amplitude of the curvature of the model surface, the number of multiple surfaces and the like, does not need to carry out mutual mapping between the two-dimensional image and the three-dimensional model, reduces interpolation calculation, obviously reduces calculation cost, effectively eliminates multi-surface reflection interference, maintains the corresponding relation between image pixel points and the model surface unchanged, and avoids additional image registration steps.
Drawings
FIG. 1 is a flow chart of a method of correcting multi-surface reflection errors facing a pressure sensitive paint measurement in an embodiment;
FIG. 2 is a schematic diagram of a model to be tested in an embodiment;
FIG. 3 is a schematic view of the light intensity distribution of an original image (with reflection errors);
FIG. 4 is a schematic diagram of the difference between the original image and the true value;
FIG. 5 is a schematic diagram showing the light intensity distribution of an original image after error correction according to the present invention;
FIG. 6 is a schematic diagram showing the difference between the original image after error correction and the true value;
Fig. 7 is a schematic diagram of an electronic device in an embodiment.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and fully with reference to the accompanying drawings, in which it is evident that the embodiments described are some, but not all embodiments of the invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the present invention without making any inventive effort, shall fall within the scope of the present invention.
Example 1
Aiming at the problems in the prior art, in order to overcome the defects of the prior art based on solving large linear equation set correction, the embodiment provides a multi-surface reflection error correction method based on pressure-sensitive paint measurement capable of micro-ray tracing, which can remove the limit on the number and curvature of three-dimensional triangular meshes, get rid of the dependence on the two-dimensional and three-dimensional mapping relation, and directly carry out pixel-by-pixel error correction based on a real shot image containing multi-surface reflection.
Referring to fig. 1, the method comprises the steps of:
s1, obtaining the reflectivity R of the pressure-sensitive paint under the wavelength of emitted light. The measurement of the reflectance R must be measured strictly in the emission band of the pressure sensitive paint.
S2, triangular mesh data of the region to be measured of the multi-surface three-dimensional model are obtained. The triangular patches should be sized to ensure that each triangular patch adequately represents the luminous intensity of its corresponding region.
S3, spraying pressure-sensitive paint on the region to be tested of the model, acquiring a luminous image Img_1 of the surface of the model under the experimental working condition by using a camera, and recording parameters of the camera
C=[Res,Pos,Look_at,fov,Up]
Where Res denotes an image resolution, pos denotes a camera position, look_at denotes a camera orientation, fov denotes a camera view angle, and Up denotes a height direction in which an image is captured by the camera.
S4, obtaining the actual luminous intensity of the triangular patches, namely initializing the luminous intensity E of all the triangular patches, obtaining a simulation image Img_2 by using a microlithography tracking technology, and continuously and iteratively updating the luminous intensity E of each triangular patch by using Img_1 as an optimization target through a counter-propagation algorithm so as to ensure that the simulation error between the image Img_2 finally obtained through simulation and the real shot image Img_1 is minimum.
Preferably, the calculation of the analog error may be performed by multi-scale gaussian filtering and downsampling to capture the difference information of the image at different resolutions, providing a more comprehensive and accurate difference metric. One specific case of analog error calculation is:
Wherein n represents the iteration times, h and w represent the pixel numbers of the original image, respectively, img_ n represents the simulation image obtained by the microlithography technique in the nth iteration, diff represents the difference image under different scales, avgPool 2×2 is an average pooling layer with the size of 2×2, gf 7×7 is a gaussian filter kernel with the size of 7×7, and uniform zero filling is performed on the image boundary during filtering (padding=3).
S5, setting the reflectivity of the pressure-sensitive paint to be zero based on the actual luminous intensity E of each triangular patch finally obtained in the step S4, and obtaining a simulation image Img_3 (namely an image corrected by reflection errors) with the surface reflection of zero by using a microlithography tracking technology.
Preferably, the calculation method based on the counter-propagating gradient may be manually fed back or automatically calculated based on an automatic differentiator (Autograd) in PyTorch. The light intensity information I of each pixel point can be expressed as
I=∫∫f(u,v;C,E)dudv
Where u and v are the abscissa and ordinate of the image pixel, respectively, and f is a scene function containing relevant parameters such as camera, model, light source, etc. Iterative optimization algorithms may be selected to include, but are not limited to, SGD, adam, etc.
The method is described below in a practical example, in which the surface pressure of the tail section of an aircraft is measured using a pressure sensitive paint technique, and the multi-surface reflection error is corrected using the method, so that the light emission true value of the pressure sensitive paint is obtained after the reflection error is corrected.
Step S1, measuring the reflectivity r=0.75 of the batch of pressure sensitive paint at the wavelength of emitted light by using an integrating sphere;
Step S2, acquiring a three-dimensional model of the tail wing part of the aircraft, and extracting three-dimensional triangular mesh data of a region to be detected, wherein a white region is an ROI region as shown in FIG. 2;
Step S3, spraying the same batch of pressure sensitive paint as in step S1 on the area to be tested of the tail wing part of the aircraft, acquiring a luminous image Img_1 (shown in figure 3, and the difference value between the luminous image and the true image is shown in figure 4) of the model surface under the experimental working condition by using a camera, and recording camera parameters
C=[Pos,Look_at,fov,Up],
Wherein the method comprises the steps of
Pos=[100,100,100];
Look_at=[0.0,0.0,-50];
fov=25;
Up=[1.00,0.0,0.0];
Step S4, initializing the luminous intensity of all triangular patches of the three-dimensional model ROI area in the step S2 to be
E0＝0.5×IN×1,
Where I N×1 denotes an identity matrix of size n×1, and n=60646 is the number of triangular patches. Taking all triangular patches as light sources, simulating and generating an image Img_2 containing multi-surface reflection, taking the Img_1 acquired in the step S3 as an optimization target, and acquiring the actual luminous intensity E 1 of each triangular patch on the surface of the model through iterative updating based on the camera parameter C recorded in the step S3 and the reflectivity R=0.75 of the pressure-sensitive paint measured in the step S1;
and S5, setting the reflectivity of the pressure-sensitive paint to be 0 based on the actual luminous intensity E 1 of each triangular surface patch of the model surface obtained in the step S5, and obtaining a luminous image under the condition of no reflection, wherein the image is an image subjected to error correction as shown in FIG. 5. At this time, the difference between the image and the true value is shown in fig. 6.
By comparing fig. 4 and fig. 6, the result corrected by the method is obviously similar to a true value without reflection, and a better error correction result of multi-surface reflection is obtained. The method obviously improves the final measurement precision through a refined error correction flow, has simple and practical whole correction process, has wide applicability, and can effectively cope with multi-surface reflection challenges of various complex models based on pressure sensitive paint measurement.
In summary, the method comprises the steps of firstly measuring the reflectivity of the current pressure-sensitive paint under the wavelength of emitted light by using an integrating sphere, obtaining three-dimensional grid data of the surface of a model, spraying the pressure-sensitive paint on the surface of the model, exciting the pressure-sensitive paint on the surface of the model by using an exciting light source under an experimental working condition, shooting, then extracting an ROI (region of interest) in an actual shooting image, recording camera parameters, and then continuously adjusting the luminous intensity of a triangular patch by iteration by taking the actual shooting image as a true value based on the recorded camera parameters and the reflectivity of the current pressure-sensitive paint under the wavelength of emitted light until the optimal luminous intensity meeting the requirement is obtained, and finally setting the reflectivity of the pressure-sensitive paint to be 0 to obtain an image with multi-surface reflection error corrected.
Compared with the traditional correction method based on the complex linear equation set, the method only needs to ensure the size and reconstruction accuracy of the three-dimensional triangular mesh of the model to be detected, has no additional limitation on factors such as the change amplitude of the model surface curvature, the number of multiple surfaces and the like, does not need to carry out mutual mapping between the two-dimensional image and the three-dimensional model, reduces interpolation calculation, and obviously reduces calculation cost. The method not only overcomes the defects of large calculated amount and more model limitation in the prior art, but also obviously improves the final measurement precision through a refined error correction flow, and the whole correction process is simple and practical, has wide applicability, can effectively cope with the multi-surface reflection challenges of various complex models based on pressure-sensitive paint measurement, and provides powerful support for realizing the measurement of high precision and high reliability of the pressure-sensitive paint.
Example 2
This embodiment provides an electronic device comprising one or more processors and memory having stored therein one or more programs including instructions for performing the method of multi-surface reflection error correction for pressure sensitive paint-facing measurements as described in embodiment 1.
Referring to fig. 7, at the hardware level, the electronic device includes a processor, an internal bus, a network interface, a memory, and a nonvolatile memory, and may of course include hardware required by other services. The processor reads the corresponding computer program from the non-volatile memory into the memory and then runs to implement the multi-surface reflection error correction method described above with respect to fig. 1. Of course, other implementations, such as logic devices or combinations of hardware and software, are not excluded from the present invention, that is, the execution subject of the following processing flows is not limited to each logic unit, but may be hardware or logic devices.
The memory may include volatile memory in a computer-readable medium, random Access Memory (RAM) and/or nonvolatile memory, such as Read Only Memory (ROM) or flash memory (flash RAM). Memory is an example of computer-readable media.
Computer readable media, including both non-transitory and non-transitory, removable and non-removable media, may implement information storage by any method or technology. The information may be computer readable instructions, data structures, modules of a program, or other data. Examples of storage media for a computer include, but are not limited to, phase change memory (PRAM), static Random Access Memory (SRAM), dynamic Random Access Memory (DRAM), other types of Random Access Memory (RAM), read Only Memory (ROM), electrically Erasable Programmable Read Only Memory (EEPROM), flash memory or other memory technology, compact disc read only memory (CD-ROM), digital Versatile Disks (DVD) or other optical storage, magnetic cassettes, magnetic disk storage or other magnetic storage devices, or any other non-transmission medium which can be used to store information that can be accessed by a computing device. Computer-readable media, as defined herein, does not include transitory computer-readable media (transmission media), such as modulated data signals and carrier waves.
Example 3
The present embodiment provides a computer-readable storage medium comprising one or more programs for execution by one or more processors of an electronic device, the one or more programs comprising instructions for performing the method of multi-surface reflection error correction for pressure-sensitive paint-oriented measurements as described in embodiment 1.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
While the invention has been described with reference to certain preferred embodiments, it will be understood by those skilled in the art that various changes and substitutions of equivalents may be made and equivalents will be apparent to those skilled in the art without departing from the scope of the invention. Therefore, the protection scope of the invention is subject to the protection scope of the claims.

Claims (8)

1.一种面向压敏涂料测量的多表面反射误差校正方法，其特征在于，包括如下步骤：1. A method for correcting multi-surface reflection errors in pressure-sensitive coating measurements, characterized by comprising the following steps: 获取压敏涂料在发射光波长的反射率；Obtain the reflectivity of the pressure-sensitive coating at the emitted light wavelength; 获取多表面待测区域的三角网格数据；Acquire triangular mesh data of the multi-surface test area; 获取喷涂有压敏涂料的所述多表面待测区域的真实发光图像，以及拍摄所述真实发光图像时的相机参数；Acquire a real luminescence image of the multi-surface test area coated with pressure-sensitive paint, and the camera parameters when capturing the real luminescence image; 基于所述三角网格数据以及所述相机参数，初始化所述待测区域中各个三角面片的发光强度，通过可微光线追踪，获取发射光波长的反射率对应的多表面待测区域的仿真图像，以最小化所述仿真图像与所述真实发光图像之间的模拟误差为目标，对仿真图像进行迭代优化；Based on the triangular mesh data and the camera parameters, the luminous intensity of each triangular facet in the region under test is initialized. By differentiable ray tracing, a simulation image of the multi-surface region under test corresponding to the reflectivity of the emitted light wavelength is obtained. With the goal of minimizing the simulation error between the simulation image and the real luminous image, the simulation image is iteratively optimized. 基于迭代优化后的仿真图像，将压敏涂料的反射率配置为零，通过可微光线追踪获取表面反射为零时的校正图像，Based on the iteratively optimized simulation image, the reflectivity of the pressure-sensitive coating is configured to zero, and a corrected image with zero surface reflection is obtained through differential ray tracing. 所述的模拟误差的计算过程包括如下步骤：The calculation process for the simulation error includes the following steps: 通过多尺度的高斯滤波和降采样，捕获仿真图像和真实发光图像在不同分辨率下的差异信息，计算模拟误差，By employing multi-scale Gaussian filtering and downsampling, the differences between simulated and real luminescent images at different resolutions are captured, and the simulation error is calculated. 所述的模拟误差采用下式计算：The simulation error is calculated using the following formula: 其中，为真实发光图像，表示第n次迭代时，利用可微光线追踪技术获取的仿真图像，表示不同尺度下的差异图像，AvgPool2×2为大小为2×2的平均池化层，gf7×7为大小为7×7的高斯滤波核，滤波时在图像边界进行均匀零填充，为填充值，h和w分别表示原始图像高和宽的像素数，为模拟误差。in, For real luminous images, This represents the simulated image obtained using differentiable ray tracing technology during the nth iteration. This represents the difference image at different scales. `AvgPool 2×2` is a 2×2 average pooling layer, and `gf 7×7` is a 7×7 Gaussian filter kernel. During filtering, uniform zero-padding is applied to the image boundaries. The values are padding values, where h and w represent the number of pixels in the height and width of the original image, respectively. This represents the simulation error. 2.根据权利要求1所述的一种面向压敏涂料测量的多表面反射误差校正方法，其特征在于，在迭代优化过程中，每个像素点的光强采用下式更新：2. The multi-surface reflection error correction method for pressure-sensitive coating measurement according to claim 1, characterized in that, during the iterative optimization process, the light intensity of each pixel is updated using the following formula: 其中，为像素点的光强信息，为包含相机、模型和光源参数的场景函数，、分别为相机参数、每个三角面片的发光强度，、分别为图像像素的横、纵坐标。in, For the light intensity information of a pixel, A scene function that includes camera, model, and light source parameters. , These are the camera parameters and the luminous intensity of each triangular facet, respectively. , These are the horizontal and vertical coordinates of the image pixels, respectively. 3.根据权利要求1所述的一种面向压敏涂料测量的多表面反射误差校正方法，其特征在于，当模拟误差小于预设阈值，或迭代次数超过设定值，终止迭代优化。3. The multi-surface reflection error correction method for pressure-sensitive coating measurement according to claim 1, characterized in that the iterative optimization is terminated when the simulation error is less than a preset threshold or the number of iterations exceeds a set value. 4.根据权利要求1所述的一种面向压敏涂料测量的多表面反射误差校正方法，其特征在于，所述的相机参数包括图像分辨率、相机位置、相机朝向、相机视场角和相机拍摄图像的高度方向。4. The method for correcting multi-surface reflection errors in pressure-sensitive coating measurement according to claim 1, wherein the camera parameters include image resolution, camera position, camera orientation, camera field of view, and the height direction of the image captured by the camera. 5.根据权利要求1所述的一种面向压敏涂料测量的多表面反射误差校正方法，其特征在于，通过配置多表面的三角面片的大小，使得每个三角面片能够反映对应区域的发光强度。5. The multi-surface reflection error correction method for pressure-sensitive coating measurement according to claim 1, characterized in that, by configuring the size of the triangular facets of the multi-surface, each triangular facet can reflect the luminous intensity of the corresponding area. 6.根据权利要求1所述的一种面向压敏涂料测量的多表面反射误差校正方法，其特征在于，所述的发射光波长的反射率的测量过程包括如下步骤：6. The multi-surface reflection error correction method for pressure-sensitive coating measurement according to claim 1, characterized in that the process of measuring the reflectivity of the emitted light wavelength includes the following steps: 利用积分球测量压敏涂料的发射光波段下的反射率。The reflectivity of pressure-sensitive coatings in the emitted light band was measured using an integrating sphere. 7.一种电子设备，其特征在于，包括：一个或多个处理器以及存储器，所述存储器内储存有一个或多个程序，所述一个或多个程序包括用于执行如权利要求1-6任一所述面向压敏涂料测量的多表面反射误差校正方法的指令。7. An electronic device, characterized in that it comprises: one or more processors and a memory, the memory storing one or more programs, the one or more programs including instructions for performing the multi-surface reflection error correction method for pressure-sensitive coating measurement as described in any one of claims 1-6. 8.一种计算机可读存储介质，其特征在于，包括供电子设备的一个或多个处理器执行的一个或多个程序，所述一个或多个程序包括用于执行如权利要求1-6任一所述面向压敏涂料测量的多表面反射误差校正方法的指令。8. A computer-readable storage medium, characterized in that it comprises one or more programs executable by one or more processors of an electronic device, said one or more programs comprising instructions for performing the multi-surface reflection error correction method for pressure-sensitive coating measurements as described in any one of claims 1-6.
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