Method and device for precise measurement of refractive index of birefringent crystal

Abstract

This application provides a method and apparatus for precise measurement of the refractive index of a birefringent crystal, relating to the field of precise crystal refractive index measurement. The method includes: acquiring the interference pattern of the birefringent crystal to be measured; obtaining high-precision center coordinates based on the interference pattern and using a convolutional neural network; extracting the time-domain light intensity signal from the high-precision center coordinates and smoothing the time-domain light intensity signal using Savitzky-Golay adaptive filtering to obtain a smoothed signal; detecting the peaks and troughs of the smoothed signal based on multi-check logic to automatically count the order of interference fringe changes; changing the optical path difference by rotating the crystal, recording the corresponding fringe change order at different rotation angles α, and calculating the ordinary and extraordinary refractive indices. This application can achieve high-precision measurement using a common rotating platform, significantly reducing experimental costs and barriers to entry.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of precise measurement of refractive index of crystal, in particular to a method and device for precise measurement of refractive index of birefringent crystal. BACKGROUND

[0002] Birefringent crystal (such as quartz, calcite, lithium niobate, etc.) is a core functional material in modern optical communication, polarization optics and laser technology. Accurate measurement of its birefringence (i.e. ordinary light refractive index and extraordinary light refractive index) is crucial for the design and performance evaluation of optical devices.

[0003] After investigation and retrieval, the existing technologies for measuring the refractive index of birefringent crystal mainly include the minimum deviation angle method and the Abbe refractometer method (critical angle method), but the above methods have significant technical defects and limitations in practical application: The minimum deviation angle method uses a spectrometer to measure the apex angle and minimum deviation angle of the prism, which is a classic method with high measurement accuracy. However, this technology has the following serious shortcomings: 1. Sample preparation is extremely difficult and destructive: This method requires the crystal to be precisely ground into a three-prism with a specific apex angle, and the crystal optical axis must be strictly parallel to the refractive prism. This not only requires high-precision cold processing technology, which is costly, but also causes irreversible damage to the sample, making it impossible to directly measure conventional crystal slices or parallel plate samples, limiting its application in industrial sampling.

[0004] 2. Instrument adjustment is complicated and costly: High-precision spectrometers have complex structures and are expensive. During the experiment, complex autocollimation adjustment is required, which requires a high level of technical expertise from the operator, making it difficult to popularize.

[0005] 3. Low discrimination of birefringence measurement: In the measurement process, the spectral lines of ordinary light and extraordinary light often appear simultaneously or overlap in the field of view, making it difficult for the observer to quickly and accurately separate and identify the two beams of polarized light, which can easily lead to confusion in the measurement data.

[0006] Abbe refractometer method: This method is based on the principle of total reflection critical angle and is a commonly used rapid measurement method, but it has obvious shortcomings in the measurement of birefringent crystals: 1. Limited measurement range and environment: Abbe refractometer usually relies on high refractive index prisms and contact liquid, and its upper limit of measurement is limited by the refractive index of the prism, making it impossible to measure high refractive index crystals. In addition, the contact liquid often has toxicity or volatile odor, which can easily contaminate the sample and pose a safety hazard to the operating environment.

[0007] 2. Blurred field of view and large subjective error in readings: For crystals with small birefringence differences, the two light-dark boundary lines in the field of view are very likely to overlap, resulting in blurred boundaries. Furthermore, this method relies entirely on human observation of the light-dark boundary lines and manual reading, lacking objective quantitative standards, leading to significant human error in judgment.

[0008] 3. Inability to automate: This device is essentially a visual optical instrument, which is difficult to directly acquire and automate signals through electronic sensors, and does not have the ability to transmit and analyze data in real time.

[0009] In summary, existing technologies generally suffer from problems such as stringent requirements on sample geometry (e.g., requiring prisms), expensive and complex instruments, and the inability to automate data acquisition and measurement processes. In particular, these existing technologies fail to meet the demands for non-destructive, rapid, intelligent, low-cost, and high-precision birefringence measurement of conventionally shaped crystals.

[0010] Therefore, there is a need for an apparatus and method for measuring the birefringence of birefringent crystals that can directly measure crystals of ordinary shapes and has anti-interference and automated measurement capabilities. Summary of the Invention

[0011] The purpose of this invention is to provide a precise method and apparatus for measuring the refractive index of birefringent crystals, in order to solve the problems of complex sample preparation, reliance on manual operation in the measurement process, and inability to achieve automation and high-precision non-destructive testing in existing birefringence measurement methods.

[0012] The above-mentioned objective of this application is achieved through the following technical solution: S1: Obtain the interference pattern of the birefringent crystal under test; S2: Based on the interferogram, a CNN-KF-ROI gradient voting fusion localization algorithm is used to obtain high-precision circle center coordinates; S3: Extract the time-domain light intensity signal of high-precision circle center coordinates, and use Savitzky-Golay adaptive filtering to smooth the time-domain light intensity signal to obtain a smooth signal; S4: Based on multiple verification logic, detect the peaks and troughs of the smooth signal and automatically count the order of interference fringe changes; S5: Change the optical path difference by rotating the birefringent crystal under test, and record different rotation angles. The ordinary and extraordinary refractive indices are calculated by determining the corresponding fringe variation order.

[0013] Optionally, the specific processing steps of the CNN-KF-ROI gradient voting fusion localization algorithm are as follows: S21: A single-channel heatmap regression network based on a modified ResNet backbone network is adopted; the interferogram of the first frame is input into the single-channel heatmap regression network, and a scaled-down two-dimensional heatmap is output. The peak coordinates of the heatmap are extracted and mapped back to the original image scale proportionally to obtain the global coarse center coordinates. S22: Initialize the state of the Kalman filter using the global coarse center coordinates; By using a Kalman filter and combining the optimal estimation state of the previous frame, the interferogram of subsequent consecutive frames is processed to obtain the predicted circular coordinates of the current frame. Using the predicted circular coordinates of the current frame as the center, a rectangular region of interest is extracted from the original high-resolution interferogram; S23: Within the region of interest, candidate regions for circle centers are obtained through edge detection and gradient voting, specifically including: The extracted region of interest is converted to grayscale, and a Gaussian filter is applied to eliminate high-frequency noise from the sensor. The Canny edge detection operator is used to extract clear interference ring edge points in the region of interest, and the Sobel operator is used to calculate the gradient of each edge point in the X and Y directions, thereby obtaining the edge normal vector. Establish a local all-zero accumulator matrix with the same size as the region of interest; by traversing all edge points, vote along the positive and negative directions of the edge point normal vector within the preset interference ring radius range, and the region with the highest number of votes in the accumulator is the candidate region for the center of the circle. S24: After finding the candidate region of the maximum value in the local all-zero accumulator matrix, take the coordinates of the candidate region of the maximum value as the center and extract a local neighborhood window of a preset size. Using the number of votes for each pixel within the local neighborhood window as weights, calculate the two-dimensional weighted centroid or perform two-dimensional Gaussian surface fitting to obtain sub-pixel-level relative coordinates with decimals. Based on the extracted sub-pixel relative coordinates and the absolute coordinate offset of the region of interest in the original image, the high-precision center coordinates of the current frame in the global image are calculated.

[0014] Optionally, the single-channel heatmap regression network based on the modified ResNet backbone network includes a single-channel grayscale input layer, an initial convolutional module, a feature extraction backbone network, a multi-level upsampling decoder, and a probability mapping output layer connected in sequence. A single-channel grayscale input layer is configured to receive a preprocessed single-channel grayscale image, with an input tensor dimension of 1×256×256. The initial convolutional module is connected to the single-channel grayscale input layer, using a 7×7 convolutional kernel with a stride of 2, zero padding of 3, and no bias term. It is used to map the single-channel grayscale image into a 64-channel shallow feature map, and the output feature map has a dimension of 64×128×128. The feature extraction backbone network is connected to the initial convolutional module. It adopts the residual structure of ResNet18, and removes its global average pooling layer and fully connected layer, removes the initial max pooling layer, and changes the convolutional stride of the first residual layer from the default 1 to 2 to extract deep semantic features layer by layer. The feature extraction backbone network includes 4 residual layers in sequence. The number of channels doubles layer by layer from 64 to 128 to 256 to 512, and the spatial resolution is halved layer by layer. The final output is a deep semantic feature map with a dimension of 512×8×8. A multi-level upsampling decoder, connected to the feature extraction backbone network, is used to progressively upsample the deep semantic feature map to restore it to the input resolution. The multi-level upsampling decoder includes: The channel-reduction convolutional layer uses a 3×3 convolutional kernel and combines batch normalization and ReLU activation function to compress the number of feature map channels from 512 to 256. The first deconvolutional layer uses transposed convolution with a kernel size of 4×4 and a stride of 4, which maps the feature map from 256×8×8 to 128×32×32. The second-level deconvolution layer uses transposed convolution with a kernel size of 4×4 and a stride of 4, which maps the feature map from 128×32×32 to 64×128×128. The third deconvolutional layer uses transposed convolution with a kernel size of 2×2 and a stride of 2, which maps the feature map from 64×128×128 to 32×256×256. A probability mapping output layer, connected to the multi-stage upsampling decoder, includes: The point convolutional layer uses a 1×1 convolutional kernel to fuse the 32-channel feature map into a single-channel feature map with a dimension of 1×256×256. The Sigmoid activation function layer is connected to the point convolutional layer to constrain the output value to the interval [0,1] and output a two-dimensional heatmap. The value of each coordinate point in the two-dimensional heatmap represents the confidence probability that the point is the center of the interference ring.

[0015] Optionally, the single-channel grayscale image received by the single-channel grayscale input layer is formed by scaling the original interference pattern to a resolution of 256×256 using bilinear interpolation.

[0016] Optionally, the two-dimensional heatmap is a subpixel-level two-dimensional Gaussian heatmap; The labels for a two-dimensional heatmap are constructed as follows: Coordinate calibration: Accurately locate the actual physical coordinates of the interference center on each scaled grayscale image; Gaussian kernel mapping: Soft labels are generated using a two-dimensional Gaussian distribution function; During the training phase of the single-channel heatmap regression network, mean squared error loss is used to calculate the pixel-level difference between the network-predicted two-dimensional heatmap and the Gaussian ground truth heatmap; the network weights are continuously updated through backpropagation algorithm until the loss function converges, thus completing the model training.

[0017] Optionally, step S4 includes: The multi-verification logic includes: Valid peak determination: The peak value is greater than 70% of the average value of all detected peak values; Valid valley determination: The valley value is less than 130% of the average of all detected valley values; Contrast verification: The difference between adjacent peaks and valleys is greater than 1.5 times the signal standard deviation or 0.2 times the global contrast.

[0018] Optionally, step S5 includes: Birefringence includes: ordinary light Refractive index and unusual light Refractive index; Ordinary light Refractive index ,as follows

[0019] Wherein, the order of the interference fringe change after the o-light is rotated is The wavelength of the light source is The rotation angle is That is, the angle of incidence; The crystal represents the angle of refraction of light within the crystal; the crystal width is... ; Unusual Light The refractive index is as follows:

[0020] Among them, e-light rotation The order of the interference fringe changes after the angle is .

[0021] A precision measuring device for the refractive index of a birefringent crystal, the device comprising: a laser source and beam expansion and collimation module, a Michelson interferometer optical path assembly, a crystal rotation and polarizing mirror selection assembly, an image acquisition module, and a processing module; The laser source and beam expanding and collimating module includes: a He-Ne laser and a beam expander; the beam expander is used to expand the point light emitted by the He-Ne laser into parallel incident light; The Michelson interferometer optical path assembly includes: a beam splitter, a compensation plate, a fixed mirror, and a movable mirror; the beam splitter is used to split the incident light into two coherent beams: reflected light and transmitted light; The crystal rotation and polarizing mirror screening assembly includes: a precision optical rotation platform, a rotatable polarizing mirror, and an observation screen; A precision optical rotating platform is set up in the optical path between the beam splitter and the fixed mirror. The birefringent crystal to be tested is fixed on the rotating platform, and the optical axis of the crystal is parallel to the rotation axis of the rotating platform (that is, the optical axis is perpendicular to the incident surface of the light). A rotatable polarizing mirror is set in front of the observation screen. By using a rotating polarizing mirror, the o-ray and e-ray, whose vibration directions are perpendicular to each other, are physically separated and made to interfere with the reference light respectively, resulting in a set of interference patterns; by rotating the precision optical rotation platform, multiple interference patterns of the birefringent crystal under test are obtained. The image acquisition module is used to acquire video streams of multiple interferometric patterns; The processing module is used to calculate the refractive index of the birefringent crystal under test based on the acquired video stream.

[0022] The image acquisition module uses a CMOS industrial camera.

[0023] The beneficial effects of the technical solution provided in this application are: Lowering the barriers to sample processing and equipment: This method only requires the crystal to be tested to have two parallel surfaces (parallel surfaces of the optical axis), without the need to process the crystal into a specific prism shape, and without the need for expensive high-precision goniometers. High-precision measurement can be achieved using only a common rotating platform, which significantly reduces experimental costs and barriers, and relaxes the restrictions on the morphology and processing accuracy of the crystal sample to be tested.

[0024] Achieving highly robust automated measurement: Innovatively introducing convolutional neural network algorithms, Savitzky-Golay filtering, and valley detection algorithms solves the problems of traditional photoelectric counting being susceptible to ambient light interference and inaccurate counting due to low fringe contrast. By introducing a time dimension through Kalman filtering, the highly complex gradient voting calculation, originally required for each full-resolution image (e.g., 1920×1080), is strictly limited to an adaptive, pixel-level micro-ROI, significantly reducing computational overhead and meeting the demands of real-time high frame rate processing. The "global noise resistance and resistance to sudden illumination changes" characteristics of CNNs are perfectly combined with the "local accuracy" characteristics of gradient voting. Even if target loss occurs during local tracking, the CNN mechanism can intervene to achieve relocation, avoiding the divergence and collapse problems common in traditional tracking algorithms. Introducing local neighborhood weighted centroid extraction at the end of the gradient voting accumulator forcibly compresses the image recognition accuracy from the usual 1-pixel error to a sub-pixel level of 0.1 pixels or even higher, providing an observation benchmark with excellent signal-to-noise ratio for subsequent brightness change extraction of interference fringes.

[0025] High precision and high efficiency: The device is highly automated and has high measurement accuracy, making it promising for application and of great practical value. Attached Figure Description

[0026] The present application will be further described below with reference to the accompanying drawings and embodiments. In the accompanying drawings: Figure 1 This is a step diagram of an embodiment of this application; Figure 2 This is a structural diagram of the device in the embodiments of this application; Figure 3 This is a schematic diagram of refractive index calculation in an embodiment of this application; Figure 4 This is a real-world structural diagram of an embodiment of this application; Figure 5 These are the actual prediction results and heat maps in the embodiments of this application; Figure 6 This is a comparison diagram of light intensity-time signals in an embodiment of this application; Figure 7 This is a graph showing the results of the quantitative analysis in the embodiments of this application. Detailed Implementation

[0027] To provide a clearer understanding of the technical features, objectives, and effects of this application, the specific embodiments of this application will now be described in detail with reference to the accompanying drawings.

[0028] The embodiments of this application provide a method for precise measurement of the refractive index of a birefringent crystal.

[0029] Please refer to Figure 1 , Figure 1 This is a flowchart illustrating the steps of a method for precise measurement of the refractive index of a birefringent crystal according to an embodiment of this application, including: S1: Obtain the interference pattern of the birefringent crystal under test; S2: Based on the interferogram, a CNN-KF-ROI gradient voting fusion localization algorithm is used to obtain high-precision circle center coordinates; S3: Extract the time-domain light intensity signal of high-precision circle center coordinates, and use Savitzky-Golay adaptive filtering to smooth the time-domain light intensity signal to obtain a smooth signal; Savitzky-Golay adaptive filter window length Based on the total length of the data Adaptive adjustment to: ,and If it is an odd number, and the calculation is... If the number is even, add 1.

[0030] In one embodiment, the system reads the video stream frame by frame and calculates the average grayscale value of all pixels within each frame region. As the crystal rotates, the center of the interference fringes exhibits a periodic alternation of "bright-dark-bright," thereby generating a light intensity fluctuation curve that varies with time t, i.e., the time-domain light intensity signal. This curve not only contains the effective interference signal but also superimposed ambient light noise and sensor thermal noise.

[0031] As one embodiment, to address the problem that traditional mean filtering or Gaussian filtering easily weakens signal peaks and leads to missed counts, this invention innovatively employs the Savitzky-Golay (SG) filtering algorithm. This algorithm, based on local polynomial least squares fitting, can effectively filter out high-frequency noise while preserving the extreme features of the signal, such as peaks and troughs, to the maximum extent.

[0032] Adaptive Window Mechanism: To adapt to the stripe variation frequency at different rotational speeds, this system introduces a dynamic window adjustment strategy. The filter window length W is adaptively set based on the total length of the acquired data. A lower limit threshold is set to prevent the window from becoming too small, which could lead to denoising failure. Technical Effect: This mechanism ensures that the data is not overly smoothed when the data volume is small (at the beginning of the experiment), and provides sufficiently strong denoising capability when the data volume is sufficient.

[0033] S4: Based on multiple verification logic, detect the peaks and troughs of the smooth signal and automatically count the order of interference fringe changes; S5: Change the optical path difference by rotating the birefringent crystal under test, and record different rotation angles. The ordinary and extraordinary refractive indices are calculated by determining the corresponding fringe variation order.

[0034] The specific processing steps of the CNN-KF-ROI gradient voting fusion localization algorithm are as follows: S21: A single-channel heatmap regression network based on a modified ResNet backbone network is adopted; the interferogram of the first frame is input into the single-channel heatmap regression network, and a scaled-down two-dimensional heatmap is output. The peak coordinates of the heatmap are extracted and mapped back to the original image scale proportionally to obtain the global coarse center coordinates. In one specific implementation of this application, the CNN initial coarse localization / anomaly wake-up process is as follows: When the system processes the first frame of the video stream, or when the tracker confidence is lower than a preset threshold (determined as target loss), the algorithm invokes a pre-trained lightweight convolutional neural network (a single-channel heatmap regression network based on a modified ResNet backbone network). The current complete frame is input into the network, and a scaled-down two-dimensional heatmap is output. The peak coordinates of the heatmap are extracted and mapped back to the original image scale proportionally to obtain the global coarse center coordinates. ; S22: Initialize the state of the Kalman filter using the global coarse center coordinates; By using a Kalman filter and combining the optimal estimation state of the previous frame, the interferogram of subsequent consecutive frames is processed to obtain the predicted circular coordinates of the current frame. Using the predicted circular coordinates of the current frame as the center, a rectangular region of interest is extracted from the original high-resolution interferogram; In one specific implementation of this application, an adaptive size mechanism is employed: the side length of the Region of Interest (ROI) is not a fixed value, but rather dynamically adjusted adaptively based on the variance of the energy distribution in the CNN output heatmap. If the energy distribution is highly concentrated (i.e., the network has high confidence in the center location), a smaller ROI is used. (pixels); if the energy distribution is diffuse or the image quality is poor, then the ROI range should be expanded accordingly ( (pixels), to ensure that the effective interference fringes are fully contained within.

[0035] S23: Within the region of interest, candidate regions for circle centers are obtained through edge detection and gradient voting, specifically including: The extracted region of interest is converted to grayscale, and a Gaussian filter is applied to eliminate high-frequency noise from the sensor. The Canny edge detection operator is used to extract clear interference ring edge points in the region of interest, and the Sobel operator is used to calculate the gradient of each edge point in the X and Y directions, thereby obtaining the edge normal vector. Establish a local all-zero accumulator matrix with the same size as the region of interest; by traversing all edge points, vote along the positive and negative directions of the edge point normal vector within the preset interference ring radius range, and the region with the highest number of votes in the accumulator is the candidate region for the center of the circle. S24: After finding the candidate region of the maximum value in the local all-zero accumulator matrix, take the coordinates of the candidate region of the maximum value as the center and extract a local neighborhood window of a preset size. Using the number of votes for each pixel within the local neighborhood window as weights, calculate the two-dimensional weighted centroid or perform two-dimensional Gaussian surface fitting to obtain sub-pixel-level relative coordinates with decimals. Based on the extracted sub-pixel relative coordinates and the absolute coordinate offset of the region of interest in the original image, the high-precision center coordinates of the current frame in the global image are calculated.

[0036] In one specific implementation of this application, a CNN-KF-ROI gradient voting fusion localization algorithm is used to perform coarse localization using a convolutional neural network, combined with Kalman filtering to predict the target region of the current frame, and high-precision circle center coordinates are obtained in the region of interest through edge detection and gradient voting calculation.

[0037] In one specific embodiment of this application, Kalman filter prediction skips the CNN full-image scanning step during normal continuous video frame processing. Instead, the Kalman filter directly predicts the prior coordinates of the interference center in the current frame based on the optimal estimated state (position and velocity) of the previous frame.

[0038] The single-channel heatmap regression network based on the modified ResNet backbone network includes a single-channel grayscale input layer, an initial convolutional module, a feature extraction backbone network, a multi-level upsampling decoder, and a probability mapping output layer connected in sequence. A single-channel grayscale input layer is configured to receive a preprocessed single-channel grayscale image, with an input tensor dimension of 1×256×256. In one specific embodiment of this application, the input reconstruction is as follows: the original image output by the interferometer mainly relies on the geometric distribution characteristics of bright and dark fringes, and the color information is redundant interference. Therefore, the network input layer is modified to receive a single-channel (1-channel) grayscale image, and the input tensor dimension is preferably set to [value missing]. (Number of channels) high width).

[0039] The initial convolutional module is connected to the single-channel grayscale input layer, using a 7×7 convolutional kernel with a stride of 2, zero padding of 3, and no bias term. It is used to map the single-channel grayscale image into a 64-channel shallow feature map, and the output feature map has a dimension of 64×128×128. The feature extraction backbone network is connected to the initial convolutional module. It adopts the residual structure of ResNet18 and removes its global average pooling layer and fully connected layer. In order to avoid the pooling layer losing the position information of interference fringes, the initial max pooling layer is removed, and the convolution stride of the first residual layer is changed from the default 1 to 2 for extracting deep semantic features layer by layer. The feature extraction backbone network includes 4 residual layers in sequence. The number of channels doubles layer by layer from 64 to 128 to 256 to 512, and the spatial resolution is halved layer by layer. The final output is a deep semantic feature map with a dimension of 512×8×8. In one specific implementation of this application, the residual structure of ResNet18 is adopted, but its original global average pooling layer and fully connected layer (Linear) used for image classification tasks are removed.

[0040] In one specific implementation of this application, the downsampling process involves the network sequentially passing through four residual layers, with the number of channels doubling layer by layer as the network deepens. The spatial resolution is halved layer by layer. The final output deep semantic feature map has a dimension of... This feature map possesses extremely strong resistance to local noise interference and global structure perception capabilities.

[0041] A multi-level upsampling decoder, connected to the feature extraction backbone network, is used to progressively upsample the deep semantic feature map to restore it to the input resolution. The multi-level upsampling decoder includes: The channel-reduction convolutional layer uses a 3×3 convolutional kernel and combines batch normalization and ReLU activation function to compress the number of feature map channels from 512 to 256. The first deconvolutional layer uses transposed convolution with a kernel size of 4×4 and a stride of 4, which maps the feature map from 256×8×8 to 128×32×32. The second-level deconvolution layer uses transposed convolution with a kernel size of 4×4 and a stride of 4, which maps the feature map from 128×32×32 to 64×128×128. The third deconvolutional layer uses transposed convolution with a kernel size of 2×2 and a stride of 2, which maps the feature map from 64×128×128 to 32×256×256. In one specific implementation of this application, the channel dimensionality reduction transition is as follows: First, a... The convolutional layer (combining BatchNorm2d and ReLU activation function) increases the number of feature map channels from Compress to This reduces the computational load of subsequent upsampling.

[0042] A probability mapping output layer, connected to the multi-stage upsampling decoder, includes: The point convolutional layer uses a 1×1 convolutional kernel to fuse the 32-channel feature map into a single-channel feature map with a dimension of 1×256×256. The Sigmoid activation function layer is connected to the point convolutional layer to constrain the output value to the interval [0,1] and output a two-dimensional heatmap. The value of each coordinate point in the two-dimensional heatmap represents the confidence probability that the point is the center of the interference ring.

[0043] In one specific implementation of this application, pixel-by-pixel regression is performed: at the end of the decoder, a... Pointwise convolution will The feature maps of the channels are fused into a single channel ( Activation constraints: Finally, the Sigmoid activation function is used to strictly constrain the output values ​​of all pixels to a certain value. The output two-dimensional matrix is ​​the "probability heatmap". The value of each coordinate in the matrix directly represents the confidence probability that the coordinate point is the center of the interference ring.

[0044] The single-channel grayscale image received by the single-channel grayscale input layer is formed by scaling the original interference pattern to a resolution of 256×256 through bilinear interpolation.

[0045] In one specific embodiment of this application, the measured data is acquired by recording interference video streams under different conditions on a Michelson interferometer platform using a mobile device. Representative video frames are extracted, covering various physical environments such as uneven illumination, strong noise, fringe distortion, and different fringe densities. Standardization processing involves converting the acquired color RGB images into single-channel grayscale images and scaling them to a fixed resolution of 256×256 using bilinear interpolation. Normalization is then performed to accelerate network convergence.

[0046] The two-dimensional heatmap is a sub-pixel level two-dimensional Gaussian heatmap; The labels for a two-dimensional heatmap are constructed as follows: Coordinate calibration: Accurately locate the actual physical coordinates of the interference center on each scaled grayscale image; Gaussian kernel mapping: Soft labels are generated using a two-dimensional Gaussian distribution function; During the training phase of the single-channel heatmap regression network, mean squared error loss is used to calculate the pixel-level difference between the network-predicted two-dimensional heatmap and the Gaussian ground truth heatmap; the network weights are continuously updated through backpropagation algorithm until the loss function converges, thus completing the model training.

[0047] In one specific implementation of this application, this step generates a 256×256 ground truth heatmap with a gradient bright spot against a completely black background. The closer to the true center, the closer the pixel value is to 1; as the distance increases, the pixel value decreases Gaussian to 0. This spatially smooth labeling effectively guides the network to learn the global convergence trend of interference fringes, rather than memorizing individual pixels.

[0048] Step S4 includes: The multi-verification logic includes: Valid peak determination: The peak value is greater than 70% of the average value of all detected peak values; Valid valley determination: The valley value is less than 130% of the average of all detected valley values; Contrast verification: The difference between adjacent peaks and valleys is greater than 1.5 times the signal standard deviation or 0.2 times the global contrast.

[0049] As one example, the system uses a dynamic threshold peak-valley detection algorithm to count the smoothed signal after SG filtering. The specific logic is as follows: Initial screening of extreme values: The difference method is used to initially extract all maximum and minimum points in the signal.

[0050] Amplitude artifact removal logic: In order to eliminate "false peaks" and "false troughs" caused by ambient light fluctuations, the system sets strict amplitude filtering conditions: Valid peak determination: The amplitude of a certain maximum point must be greater than 70% of the average of all detected peaks.

[0051] Valid valley determination: The amplitude of a certain minimum point must be less than 130% of the average of all detected valley values.

[0052] Contrast and saliency verification: Calculate the brightness difference between adjacent peak-valley pairs, and retain only extreme value pairs whose brightness difference is greater than 1.5 times the signal standard deviation or 0.2 times the global contrast. This step can effectively filter out misjudgments caused by low stripe contrast or local spot flicker.

[0053] Logical compensation count: Counts the number of valid peak-valley alternations selected in the final screening.

[0054] Boundary correction: Considering that the fringes may be in half a cycle when the experiment stops (e.g., the beginning and end are peaks and troughs respectively), the system detects the type of extreme values ​​at the beginning and end. If the types are different, the final fringe order is determined. +0.5, if the types are the same, then the final stripe level. This further improves measurement accuracy.

[0055] Step S5 includes: Birefringence includes: ordinary light Refractive index and unusual light Refractive index; Ordinary light Refractive index The derivation of the formula:

[0056] ,

[0057]

[0058]

[0059] The final result is:

[0060] The optical path difference before and after the rotation of the o-light is: The order of the interference fringes change after the o-light is rotated is The wavelength of the light source is ; This represents the actual path length of light propagation within the crystal. This represents the optical path length from the crystal's exit point to the mirror; the distance from the crystal to the plane mirror before rotation is... The rotation angle is That is, the angle of incidence; The crystal represents the angle of refraction of light within the crystal; the crystal width is... ; Let n be the refractive index of air, and n=1. Unusual Light The refractive index is as follows:

[0061] Among them, e-light rotation The order of the interference fringe changes after the angle is .

[0062] In one specific implementation of this application, such as Figure 3 As shown, rotating the optical rotating platform changes the incident angle of light with the crystal surface, thus altering the propagation path of the subsequent light. Compared to before rotation, the optical path difference changes, resulting in a change in the interference pattern. The solution is obtained by analyzing the interference pattern. , .

[0063] This invention is based on the Michelson-Morley interference principle in physical optics, combined with the birefringence effect in crystal optics, to measure the refractive index by precisely rotating and modulating the optical path difference. For example... Figure 2 As shown, the specific working principle is explained in detail below: 1. Construction of the interference optical path and formation of equal-inclination interference fringes The optical path of this device is based on a Michelson interferometer architecture. The monochromatic light emitted by the He-Ne laser (wavelength) After passing through the beam expansion and collimation system, a relatively wide parallel beam is formed and projected onto the beam splitter (G1).

[0064] The beam splitter G1 divides the incident beam into two coherent beams according to their amplitude: one beam is the reflected beam (beam 1), which is directed toward the fixed mirror M1; the other beam is the transmitted beam (beam 2), which is directed toward the movable mirror M2.

[0065] The sample to be tested is a parallel-plate birefringent crystal (optical axis parallel to the crystal surface), placed in the path of beam 2 (i.e., between M2 and G1). According to the principles of crystal optics, when beam 2 enters the birefringent crystal, it will decompose into two linearly polarized beams with mutually perpendicular vibration directions: the ordinary ray (o ray) and the extraordinary ray (e ray). The two have different refractive indices within the crystal (respectively...). and The propagation speeds are different, which results in phase delay.

[0066] At this point, the o-ray, e-ray, and the initially reflected light (beam 1) finally enter the observation screen. The interference field on the observation screen actually contains a superposition of the o-ray interference pattern and the e-ray interference pattern, which is difficult to distinguish through direct measurement. This invention places a rotatable polarizing mirror in front of the observation screen. Utilizing Malus's Law and the orthogonality of polarized light, the measurement... When: Rotate the polarizing filter so that its transmission direction is parallel to the vibration direction of the o-ray from the crystal. At this point, the e-ray is filtered out, and a clear, independent o-ray interference pattern appears on the observation screen. Similarly, in measurement... At this point, continue rotating the polarizing mirror by 90 degrees so that its transmission direction is parallel to the e-ray. At this time, the o-ray is filtered out, and the interference pattern of the e-ray is presented.

[0067] This physical separation simplifies the complex polychromatic interference problem into a single-wavelength, single-polarization interference problem.

[0068] Since the crystal is placed on a precision rotating platform, the optical path difference changes when the birefringent crystal under test is rotated, thus changing the interference pattern. The relationship between the optical path difference, the order of change in the interference pattern, the rotation angle, and the refractive index can be established to solve for the refractive index. This is because the order of change in the interference fringes... When determining this, the rotation angle can be recorded. To the refractive index Take measurements.

[0069] 2. Automated counting and stripe throughput phenomenon: With rotation angle The increase in optical path difference Continuously changing. Each time the optical path difference changes by one wavelength... The bright and dark spots at the center of the interference fringes will alternate once (i.e., "swallow" or "spit out" a ring), and the corresponding fringe change order will increase by 1.

[0070] This invention uses the aforementioned automated system to monitor the changes in light intensity at the center of the interference pattern in real time, accurately record the fringe variation order, separate the interference patterns of the o-ray and e-ray using a polarizing mirror, analyze their interference patterns separately, and record their corresponding rotation termination angles. Multiple groups Substituting the data into the above equation, the birefringence of the birefringent crystal under test can be solved in reverse.

[0071] A precision measuring device for the refractive index of a birefringent crystal, the device comprising: a laser source and beam expansion and collimation module, a Michelson interferometer optical path assembly, a crystal rotation and polarizing mirror selection assembly, an image acquisition module, and a processing module; The laser source and beam expanding and collimating module includes: a He-Ne laser and a beam expander; the beam expander is used to expand the point light emitted by the He-Ne laser into parallel incident light; The Michelson interferometer optical path assembly includes: a beam splitter, a compensation plate, a fixed mirror, and a movable mirror; the beam splitter is used to split the incident light into two coherent beams: reflected light and transmitted light; The crystal rotation and polarizing mirror screening assembly includes: a precision optical rotation platform, a rotatable polarizing mirror, and an observation screen; A precision optical rotating platform is set up in the optical path between the beam splitter and the fixed mirror. The birefringent crystal to be tested is fixed on the rotating platform, and the optical axis of the crystal is parallel to the rotation axis of the rotating platform. A rotatable polarizing mirror is set in front of the observation screen. By using a rotating polarizing mirror, the o-ray and e-ray, whose vibration directions are perpendicular to each other, are physically separated and made to interfere with the reference light respectively, resulting in a set of interference patterns; by rotating the precision optical rotation platform, multiple interference patterns of the birefringent crystal under test are obtained. The image acquisition module is used to acquire video streams of multiple interferometric patterns; The processing module is used to calculate the refractive index of the birefringent crystal under test based on the acquired video stream.

[0072] The image acquisition module uses a CMOS industrial camera.

[0073] like Figure 4 As shown, Figure 4 This is a real-world structural image of a precision refractive index measurement device for birefringent crystals. The image acquisition module includes, but is not limited to, mobile phone cameras and CMOS industrial cameras.

[0074] like Figure 5 As shown, the green text "pred: (x, y)" in the upper left corner of the prediction result image on the left represents the center coordinates of the circle output by the model. The red dot at the very center of the image is the position of the center coordinates predicted by the model on the physical image. The model can effectively overcome the inherent interference of grid lines in the background and uneven illumination distribution, accurately locking the convergence center of the interference fringes.

[0075] Figure 5 The heatmap on the right shows large areas of dark blue, representing "extremely low confidence probability" that the network believes the center of the interference circle exists in those areas. The bright (cyan / bright yellow) gradient spots in the image indicate that the network is highly confident that the interference center is located there. Instead of using easily divergent direct numerical regression, Gaussian heatmap regression was employed. By finding the maximum energy peak point in the heatmap and mapping it back to the original image, the coordinates in the pred image were obtained. This method exhibits extremely strong noise resistance.

[0076] Figure 6 This is a comparison diagram of light intensity-time signals in an embodiment of this application; like Figure 6The image shows a comparison of light intensity-time signals obtained by locating the center of a circle in the same video using a pure convolutional neural network algorithm and the hybrid localization algorithm of this invention. Based on the actual physical truth value precisely calibrated by the human eye, the interference fringe variation order (14 levels) obtained by the hybrid localization algorithm proposed in this invention is completely consistent with the actual physical truth value, effectively overcoming the miscounting problem caused by integer pixel jumps in a single CNN algorithm.

[0077] Figure 7 This is a graph showing the results of quantitative analysis in the embodiments of this application; like Figure 7 As shown in the figure, this diagram presents the results of quantization analysis of the light intensity / time signal maps obtained after locating the same video center using both a pure convolutional neural network algorithm and the hybrid algorithm of this invention. Experimental data demonstrates that, compared to the pure convolutional neural network algorithm, the hybrid localization algorithm of this invention achieves a significant improvement in signal-to-noise ratio (SNR) while effectively reducing noise variance and smoothness variance. These quantization results fully demonstrate the noise resistance and high stability of this invention in sub-pixel-level tracking and extraction.

[0078] The above are merely exemplary embodiments of this disclosure and should not be construed as limiting the scope of this disclosure. Any equivalent changes and modifications made in accordance with the teachings of this disclosure shall still fall within the scope of this disclosure.

[0079] This application is intended to cover any variations, uses, or adaptations of this disclosure that follow the general principles of this disclosure and include common knowledge or customary techniques in the art not described in this disclosure. The specification and embodiments are to be considered exemplary only, and the scope and spirit of this disclosure are defined by the claims.

Claims

1. A method for precise measurement of the refractive index of a birefringent crystal, characterized in that, The method includes: S1: Obtain the interference pattern of the birefringent crystal under test; S2: Based on the interferogram, a CNN-KF-ROI gradient voting fusion localization algorithm is used to obtain high-precision circle center coordinates; S3: Extract the time-domain light intensity signal of high-precision circle center coordinates, and use Savitzky-Golay adaptive filtering to smooth the time-domain light intensity signal to obtain a smooth signal; S4: Based on multiple verification logic, detect the peaks and troughs of the smooth signal and automatically count the order of interference fringe changes; S5: Change the optical path difference by rotating the birefringent crystal under test, and record different rotation angles. The ordinary and extraordinary refractive indices are calculated by determining the corresponding fringe variation order.

2. The method for precise measurement of the refractive index of a birefringent crystal as described in claim 1, characterized in that, The specific processing steps of the CNN-KF-ROI gradient voting fusion localization algorithm are as follows: S21: A single-channel heatmap regression network based on a modified ResNet backbone network is adopted; the interferogram of the first frame is input into the single-channel heatmap regression network, and a scaled-down two-dimensional heatmap is output. The peak coordinates of the heatmap are extracted and mapped back to the original image scale proportionally to obtain the global coarse center coordinates. S22: Initialize the state of the Kalman filter using the global coarse center coordinates; By using a Kalman filter and combining the optimal estimation state of the previous frame, the interferogram of subsequent consecutive frames is processed to obtain the predicted circular coordinates of the current frame. Using the predicted circular coordinates of the current frame as the center, a rectangular region of interest is extracted from the original high-resolution interferogram; S23: Within the region of interest, candidate regions for circle centers are obtained through edge detection and gradient voting, specifically including: The extracted region of interest is converted to grayscale, and a Gaussian filter is applied to eliminate high-frequency noise from the sensor. The Canny edge detection operator is used to extract clear interference ring edge points in the region of interest, and the Sobel operator is used to calculate the gradient of each edge point in the X and Y directions, thereby obtaining the edge normal vector. Establish a local all-zero accumulator matrix with the same size as the region of interest; by traversing all edge points, vote along the positive and negative directions of the edge point normal vector within the preset interference ring radius range, and the region with the highest number of votes in the accumulator is the candidate region for the center of the circle. S24: After finding the candidate region of the maximum value in the local all-zero accumulator matrix, take the coordinates of the candidate region of the maximum value as the center and extract a local neighborhood window of a preset size. Using the number of votes for each pixel within the local neighborhood window as weights, calculate the two-dimensional weighted centroid or perform two-dimensional Gaussian surface fitting to obtain sub-pixel-level relative coordinates with decimals. Based on the extracted sub-pixel relative coordinates and the absolute coordinate offset of the region of interest in the original image, the high-precision center coordinates of the current frame in the global image are calculated.

3. The method for precise measurement of the refractive index of a birefringent crystal as described in claim 2, characterized in that, The single-channel heatmap regression network based on the modified ResNet backbone network includes a single-channel grayscale input layer, an initial convolutional module, a feature extraction backbone network, a multi-level upsampling decoder, and a probability mapping output layer connected in sequence. A single-channel grayscale input layer is configured to receive a preprocessed single-channel grayscale image, with an input tensor dimension of 1×256×256. The initial convolutional module is connected to the single-channel grayscale input layer, using a 7×7 convolutional kernel with a stride of 2, zero padding of 3, and no bias term. It is used to map the single-channel grayscale image into a 64-channel shallow feature map, and the output feature map has a dimension of 64×128×128. The feature extraction backbone network is connected to the initial convolutional module. It adopts the residual structure of ResNet18, and removes its global average pooling layer and fully connected layer, removes the initial max pooling layer, and changes the convolutional stride of the first residual layer from the default 1 to 2 to extract deep semantic features layer by layer. The feature extraction backbone network includes 4 residual layers in sequence. The number of channels doubles layer by layer from 64 to 128 to 256 to 512, and the spatial resolution is halved layer by layer. The final output is a deep semantic feature map with a dimension of 512×8×8. A multi-level upsampling decoder, connected to the feature extraction backbone network, is used to progressively upsample the deep semantic feature map to restore it to the input resolution. The multi-level upsampling decoder includes: The channel-reduction convolutional layer uses a 3×3 convolutional kernel and combines batch normalization and ReLU activation function to compress the number of feature map channels from 512 to 256. The first deconvolutional layer uses transposed convolution with a kernel size of 4×4 and a stride of 4, which maps the feature map from 256×8×8 to 128×32×32. The second-level deconvolution layer uses transposed convolution with a kernel size of 4×4 and a stride of 4, which maps the feature map from 128×32×32 to 64×128×128. The third deconvolutional layer uses transposed convolution with a kernel size of 2×2 and a stride of 2, which maps the feature map from 64×128×128 to 32×256×256. The probability mapping output layer, connected to the multi-stage upsampling decoder, includes: The point convolutional layer uses a 1×1 convolutional kernel to fuse the 32-channel feature map into a single-channel feature map with a dimension of 1×256×256. The Sigmoid activation function layer is connected to the point convolutional layer to constrain the output value to the interval [0,1] and output a two-dimensional heatmap. The value of each coordinate point in the two-dimensional heatmap represents the confidence probability that the point is the center of the interference ring.

4. The method for precise measurement of the refractive index of a birefringent crystal as described in claim 3, characterized in that, The single-channel grayscale image received by the single-channel grayscale input layer is formed by scaling the original interference pattern to a resolution of 256×256 through bilinear interpolation.

5. The method for precise measurement of the refractive index of a birefringent crystal as described in claim 2, characterized in that, The two-dimensional heatmap is a sub-pixel level two-dimensional Gaussian heatmap; The labels for a two-dimensional heatmap are constructed as follows: Coordinate calibration: Accurately locate the actual physical coordinates of the interference center on each scaled grayscale image; Gaussian kernel mapping: Soft labels are generated using a two-dimensional Gaussian distribution function; During the training phase of the single-channel heatmap regression network, mean squared error loss is used to calculate the pixel-level difference between the network-predicted two-dimensional heatmap and the Gaussian ground truth heatmap; the network weights are continuously updated through backpropagation algorithm until the loss function converges, thus completing the model training.

6. The method for precise measurement of the refractive index of a birefringent crystal as described in claim 1, characterized in that, Step S4 includes: The multi-verification logic includes: Valid peak determination: The peak value is greater than 70% of the average value of all detected peak values; Valid valley determination: The valley value is less than 130% of the average of all detected valley values; Contrast verification: The difference between adjacent peaks and valleys is greater than 1.5 times the signal standard deviation or 0.2 times the global contrast.

7. The method for precise measurement of the refractive index of a birefringent crystal as described in claim 1, characterized in that, Step S5 includes: Birefringence includes: ordinary light Refractive index and unusual light Refractive index; Ordinary light Refractive index ,as follows Wherein, the order of the interference fringe change after the o-light is rotated is The wavelength of the light source is The rotation angle is That is, the angle of incidence; The crystal represents the angle of refraction of light within the crystal; the crystal width is... ; Unusual Light The refractive index is as follows: Among them, e-light rotation The order of the interference fringe changes after the angle is .

8. A precision measuring device for the refractive index of a birefringent crystal, used to implement the precision measuring method for the refractive index of a birefringent crystal as described in any one of claims 1-7, characterized in that, The device includes: a laser source and beam expansion and collimation module, a Michelson interferometer optical path assembly, a crystal rotation and polarization mirror selection assembly, an image acquisition module, and a processing module; The laser source and beam expanding and collimating module includes: a He-Ne laser and a beam expander; the beam expander is used to expand the point light emitted by the He-Ne laser into parallel incident light; The Michelson interferometer optical path assembly includes: a beam splitter, a compensation plate, a fixed mirror, and a movable mirror; the beam splitter is used to split the incident light into two coherent beams: reflected light and transmitted light; The crystal rotation and polarizing mirror screening assembly includes: a precision optical rotation platform, a rotatable polarizing mirror, and an observation screen; A precision optical rotating platform is set up in the optical path between the beam splitter and the fixed mirror. The birefringent crystal to be tested is fixed on the rotating platform, and the optical axis of the crystal is parallel to the rotation axis of the rotating platform. A rotatable polarizing mirror is set in front of the observation screen. By using a rotating polarizing mirror, the o-ray and e-ray, whose vibration directions are perpendicular to each other, are physically separated and made to interfere with the reference light respectively, resulting in a set of interference patterns; by rotating the precision optical rotation platform, multiple interference patterns of the birefringent crystal under test are obtained. The image acquisition module is used to acquire video streams of multiple interferometric patterns; The processing module is used to calculate the refractive index of the birefringent crystal under test based on the acquired video stream.

9. The precision measuring device for the refractive index of a birefringent crystal as described in claim 8, characterized in that, The image acquisition module uses a CMOS industrial camera.

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