Michelson interferometer and micro-part morphology detection method

Abstract

The present application discloses a Michelson interferometer and a method for detecting the morphology of a micro-device. The interferometer includes two interference light paths. In the first interference light path, the light beam of the first light source is split by the first beam splitter, one beam is reflected to the object to be measured, and the other beam is transmitted to the first test reflector. The two beams of light return to the first beam splitter respectively to interfere, and the first image acquisition system receives the first interference image; in the second interference light path, the light beam of the second light source is split by the second beam splitter, one beam is reflected to the calibration reflector, and the other beam is transmitted to the second test reflector. The two beams of light return to the second beam splitter respectively to interfere, and the second image acquisition system receives the second interference image; the two interference light paths share the same piezoelectric ceramic, and the piezoelectric ceramic controls the displacement of the first test reflector and the second test reflector. The present application can correct the first interference image based on the second interference image, perform image restoration based on the corrected first interference image, and obtain the surface morphology of the object to be measured.

Description

Technical Field

[0001] The present application relates to the field of optical measurement technology, and in particular to a Michelson interferometer and a method for detecting the morphology of small parts. Background Art

[0002] Piezoelectric ceramics are precision devices that generate micro-displacement creep under voltage control. Affected by external factors such as temperature and vibration, their elongation can change from a linear relationship to a nonlinear relationship with voltage changes, affecting the step length in the Michelson interferometer system and, consequently, the phase difference of the interference image of the object being measured captured by the image acquisition system. Most existing optical interferometry systems for measuring the topography of tiny devices using piezoelectric ceramic controllers utilize only a micro-nanoscale rotation stage for 360° manual rotation and an adjustable tilt stage. This reduces external interference through the piezoelectric ceramic structure, making real-time data feedback and error analysis impossible during use. This results in low accuracy in the interference image of the object being measured. Summary of the Invention

[0003] In order to solve the deficiencies of the prior art, this application adopts the following technical solutions:

[0004] In a first aspect, the present application provides a Michelson interferometer, comprising:

[0005] A first Michelson interferometer optical path includes a first light source, a workbench, a first beam splitter, a first test reflector, and a first image acquisition system. The workbench is used to place an object to be measured. The light beam emitted by the first light source is split by the first beam splitter. One beam is reflected onto the surface of the object to be measured, and the other beam is transmitted to the first test reflector. The two beams are reflected by the object to be measured and the first test reflector respectively and return, interfering at the first beam splitter. The first image acquisition system receives a first interference image.

[0006] A second Michelson interferometer optical path includes a second light source, a calibration reflector, a second beam splitter, a second test reflector, and a second image acquisition system. The light beam emitted by the second light source is split by the second beam splitter, one beam is reflected onto the surface of the calibration reflector, and the other beam is transmitted to the second test reflector. The two beams are reflected by the calibration reflector and the second test reflector respectively and return, interfering at the second beam splitter. The second image acquisition system receives a second interference image.

[0007] The first Michelson interference optical path and the second Michelson interference optical path share the same piezoelectric ceramic, and the piezoelectric ceramic is configured to control the displacement of the first test reflector and the second test reflector.

[0008] In summary, the present application provides a Michelson interferometer, which ensures the synchronization of the displacement of the first Michelson interferometer optical path as a measurement system and the second Michelson interferometer optical path as a calibration system by sharing the same piezoelectric ceramic through the first Michelson interferometer optical path and the second Michelson interferometer optical path, so that the phase change of the second interference image obtained by the second Michelson interferometer optical path can accurately reflect the actual phase data of the first Michelson interferometer optical path, correct the first interference image based on the obtained second interference image, and restore the image based on the corrected first interference image, finally obtaining the accurate surface morphology of the object to be measured, realizing real-time data feedback and error calibration during the detection process, and improving the accuracy and reliability of the morphology detection of tiny devices.

[0009] Furthermore, the second light source is configured as a helium-neon laser to eliminate the dispersion effect in the second Michelson interference optical path;

[0010] The Michelson interferometer further includes a processing module configured to perform phase analysis on the second interference image by a principal component analysis method to obtain a wrapped phase map, wherein the wrapped phase map includes the wrapped phases of different pixels of the second interference image, and perform phase unwrapping on the wrapped phase map by a path tracking method to obtain true absolute phases of different pixels;

[0011] The processing module performs phase compensation on the first interference image based on the true absolute phase, regenerates a uniform interference image, and performs image restoration based on the regenerated uniform interference image to obtain the surface morphology of the object to be measured.

[0012] Furthermore, the processing module performs phase analysis on the second interference image by using a principal component analysis method, including:

[0013] constructing an original data matrix based on the plurality of second interference images acquired by the second image acquisition system;

[0014] Subtracting the background light intensity from the original data matrix to obtain the AC component matrix of the interference fringes;

[0015] Perform singular value decomposition on the AC component matrix,

[0016] The principal components are selected based on the singular value decomposition results. The residual of the background light intensity is selected as the first principal component, the spatial distribution of the cosine component of the phase information is selected as the second principal component, and the spatial distribution of the sine component of the phase information is selected as the third principal component.

[0017] The selected principal components are vectorized, and the wrapped phase map is obtained based on the vectorization result.

[0018] Furthermore, the processing module performs phase unwrapping on the wrapped phase image by a path tracking method, including:

[0019] Performing a quality assessment on the availability of pixels in the wrapped phase image, obtaining quality factors of pixels in different regions of the wrapped phase image, and generating a quality map based on the quality factors;

[0020] A priority queue of different regions of the wrapped phase image is constructed based on the quality factor. According to the priority queue, regions with higher priority are iteratively unwrapped to obtain the true absolute phase of each pixel point in different regions.

[0021] Furthermore, the processing module is further configured to, when performing phase unwrapping, if the height and phase relationship of the object to be measured satisfies: , then add a curvature constraint to the height of the object to be measured, and the curvature constraint is expressed by the following formula:

[0022] ;

[0023] Where λ represents the wavelength of the second light source, h ( x , y ) represents the coordinates ( x , y ) at the height of the object to be measured, Represents a pixel ( x , y ), and k represents the curvature constraint.

[0024] Furthermore, the processing module performs phase compensation on the first interference image in the first Michelson interference optical path based on the true absolute phase to regenerate a uniform interference image, including:

[0025] According to the true absolute phase of each pixel, the phase compensation value of different pixels is calculated by the following formula:

[0026] ;

[0027] Where, is the standard displacement of the piezoelectric ceramic controller, , is the actual displacement of the piezoelectric ceramic, λ represents the wavelength of the second light source, Indicates the true absolute phase of the pixel,

[0028] Based on the phase compensation value, phase compensation is performed on the pixel points of corresponding coordinates in the first interference image to regenerate a uniform interference image.

[0029] Furthermore, the processing module performs phase compensation on the pixel points of corresponding coordinates in the first interference image using the following formula:

[0030] ;

[0031] Where, Indicates the grayscale value of the pixel after compensation, represents the DC component of the background light intensity in the first Michelson interference optical path, represents the modulation amplitude of the first Michelson interference optical path, represents the uncompensated gray value of the first interference image pixel, Indicates the standard displacement of the piezoelectric ceramic controller.

[0032] Furthermore, the processing module is further configured to: generate interference curves of different pixel points based on corresponding pixel points in the plurality of uniform interference images,

[0033] Selecting some of the interference curves as normal interference curves, and generating a reference distribution based on the selected normal interference curves;

[0034] A two-sample normality test is used to screen interference curves whose curve distribution is the same or similar to the reference distribution from the remaining interference curves to generate a new data set. Image restoration is performed based on the new data set to obtain the surface morphology of the object to be measured.

[0035] Furthermore, the first light source is configured as white light.

[0036] In a second aspect, the present application further provides a method for detecting the morphology of a micro device, the method using the above-mentioned Michelson interferometer, the method comprising the following steps:

[0037] performing phase analysis on the second interference image by a principal component analysis method to obtain a wrapped phase map, wherein the wrapped phase map includes the wrapped phases of different pixels of the second interference image, and performing phase unwrapping on the wrapped phase map by a path tracing method to obtain true absolute phases of different pixels;

[0038] Based on the true absolute phase, phase compensation is performed on the first interference image to regenerate a uniform interference image, and image restoration is performed based on the regenerated uniform interference image to obtain the surface morphology of the object to be measured. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 A schematic structural diagram of a Michelson interferometer provided in one embodiment of the present application;

[0040] Figure 2A flowchart of the steps for a processing module in a Michelson interferometer to obtain the surface morphology of an object to be measured provided in one embodiment of the present application;

[0041] Figure 3 A flowchart of the steps for obtaining a wrapped phase image by a processing module in a Michelson interferometer provided in one embodiment of the present application;

[0042] Figure 4 A flowchart of the steps for obtaining the true absolute phase of different pixel points by a processing module in a Michelson interferometer provided in one embodiment of the present application;

[0043] Figure 5 A flowchart of the steps for a processing module in a Michelson interferometer to regenerate a uniform interference image according to one embodiment of the present application;

[0044] Figure 6 A flowchart of the steps of performing image restoration based on the regenerated uniform interference image by a processing module in a Michelson interferometer provided in one embodiment of the present application;

[0045] Figure 7 A schematic diagram of an interference curve of a normal pixel point in a Michelson interferometer provided in one embodiment of the present application;

[0046] Figure 8 A schematic diagram of an interference curve of a noise pixel point in a Michelson interferometer provided in one embodiment of the present application;

[0047] Figure 9 A schematic diagram of fitting an interference curve using a quadratic Gaussian function in a Michelson interferometer provided by one embodiment of the present application;

[0048] Figure 10 A flowchart of the steps of a method for detecting the morphology of a micro device provided in one embodiment of the present application. DETAILED DESCRIPTION

[0049] The present application will be described in detail below in conjunction with the specific embodiments shown in the accompanying drawings, but these embodiments do not limit the present application. Structural, methodological, or functional changes made by ordinary technicians in this field based on these embodiments are included in the scope of protection of the present application.

[0050] In order to solve the shortcomings of the existing technology, firstly, Figure 1As shown, the present application provides a Michelson interferometer 100, which includes a first Michelson interference optical path 11, a second Michelson interference optical path 12, and a piezoelectric ceramic 13. The first Michelson interference optical path 11 includes a first light source 111, a workbench 112, a first beam splitter 113, a first test reflector 114, and a first image acquisition system 115. The workbench 112 is used to place the object to be tested. The light beam emitted by the first light source 111 is split by the first beam splitter 113. One beam is reflected onto the surface of the object to be tested, and the other beam is transmitted to the first test reflector 114. The two beams are reflected by the object to be tested and the first test reflector 114 respectively and return. They interfere at the first beam splitter 113, and the first image acquisition system 115 receives the first interference image.

[0051] The second Michelson interferometer optical path 12 includes a second light source 121, a calibration mirror 122, a second beam splitter 123, a second test mirror 124, and a second image acquisition system 125. The light beam emitted by the second light source 121 is split by the second beam splitter 123. One beam is reflected onto the surface of the calibration mirror 122, and the other is transmitted to the second test mirror 124. The two beams are reflected back by the calibration mirror 122 and the second test mirror 124, respectively, and interfere with each other at the second beam splitter 123. The second image acquisition system 125 receives the second interference image. The first Michelson interferometer optical path 11 and the second Michelson interferometer optical path 12 share the same piezoelectric ceramic 13, which is configured to control the displacement of the first test mirror 114 and the second test mirror 124.

[0052] Specifically, in the first Michelson interferometer optical path 11, a workbench 112 ensures that the object under test remains in a fixed position during measurement. A first light source 111 emits a light beam, which is split into two beams by a first beam splitter 113. One beam is reflected onto the surface of the object under test on the workbench 112, while the other is transmitted to a first test reflector 114. The first test reflector 114 is connected to a piezoelectric ceramic 13. Voltage controls the piezoelectric ceramic 13 to produce a small displacement, which in turn controls the first test reflector 114 to also slightly displace the first test reflector 114, thereby changing the optical path difference of the reference optical path. After reflecting from the object under test and the first test reflector 114, the two beams from the first light source 111 return to the first beam splitter 113, where they reunite and interfere, forming interference fringes. A first image acquisition system 115 (e.g., a CCD grayscale camera) captures the surface of the object under test to generate a first interference image. Based on this first interference image, an interference curve is subsequently constructed by extracting the grayscale values of pixels at the same location in different interference images. This curve is used to analyze the relative height values of these pixels, providing a data foundation for surface topography detection. Optionally, in the embodiment of the present application, the resolution of the first interference image is 1344×564 pixels.

[0053] In the second Michelson interference optical path 12, the light beam emitted by the second light source 121 is split by the second beam splitter 123. One beam is reflected onto the surface of the calibration mirror 122, and the other beam is transmitted to the second test mirror 124. The second test mirror 124 is connected to the piezoelectric ceramic 13. Voltage is used to control the piezoelectric ceramic 13 to produce a small displacement, which in turn controls the second test mirror 124 to also slightly displace, thereby changing the optical path difference of the reference optical path. The two beams reflected from the second light source 121 are reflected by the calibration mirror 122 and the second test mirror 124, respectively, and then return to the second beam splitter 123, where they interfere and form interference fringes. The second image acquisition system 125 (such as a CCD grayscale camera) captures and obtains a second interference image, which provides calibration data for subsequent phase compensation of the first interference image.

[0054] Furthermore, the first test reflector 114 of the first Michelson interference optical path 11 and the second test reflector 124 of the second Michelson interference optical path 12 share the same piezoelectric ceramic 13. The driving mechanism of the piezoelectric ceramic 13 is based on the inverse piezoelectric effect: when voltage is applied, the piezoelectric ceramic 13 deforms, thereby driving the first test reflector 114 and the second test reflector 124 to move synchronously, synchronously changing the optical path difference between the two optical paths.

[0055] According to the above description, the present application provides a Michelson interferometer, which ensures the synchronization of the displacement of the first Michelson interferometer as a measurement system and the second Michelson interferometer as a calibration system by sharing the same piezoelectric ceramic through the first Michelson interferometer optical path and the second Michelson interferometer optical path, so that the phase change of the second interference image obtained by the second Michelson interferometer optical path can accurately reflect the actual phase data of the first Michelson interferometer optical path, correct the first interference image based on the obtained second interference image, and restore the image based on the corrected first interference image, finally obtaining the accurate surface morphology of the object to be measured, realizing real-time data feedback and error calibration during the detection process, and improving the accuracy and reliability of the morphology detection of tiny devices.

[0056] As an optional implementation, the first light source is configured as a white light source. White light has large dispersion, which facilitates obtaining interference information by locating the zero optical path difference position. The second light source uses a helium-neon laser with a wavelength of 632.8nm. Helium-neon lasers are monochromatic and highly coherent, eliminating the influence of dispersion and allowing direct phase calculation. This eliminates the influence of dispersion in the second Michelson interferometer optical path and avoids the complex process of locating the zero optical path difference position in white light interferometry.

[0057] As an optional implementation, the Michelson interferometer provided in this application further includes a processing module, which obtains the surface morphology of the object to be measured through the following steps: Figure 2 As shown, the specific steps include:

[0058] Step S101 : performing phase analysis on the second interference image by principal component analysis to obtain a wrapped phase map, where the wrapped phase map includes wrapped phases of different pixel points of the second interference image.

[0059] Step S102 : performing phase unwrapping on the wrapped phase image by a path tracing method to obtain the true absolute phases of different pixel points.

[0060] Step S103 : The processing module performs phase compensation on the first interference image based on the true absolute phase to regenerate a uniform interference image.

[0061] Step S104 : performing image restoration based on the regenerated uniform interference image to obtain the surface topography of the object to be measured.

[0062] Specifically, in step S101, a background image without light interference is taken in advance, and the light intensity value is analyzed to obtain the background light intensity. The wrapped phase information is extracted from the second interference image through principal component analysis. The multiple second interference images collected when the piezoelectric ceramic drives the second test reflector to move are stacked into a matrix. The pre-obtained background light intensity is subtracted from this matrix to obtain a matrix containing the AC component of the interference fringes. Principal component analysis is performed on the matrix containing the AC component of the interference fringes to separate the different principal components, and finally a wrapped phase map is generated through vectorization processing. The wrapped phase map includes the wrapped phases of different pixels in the second interference image, providing the raw data basis for subsequent unwrapping.

[0063] After obtaining the wrapped phase image, in step S102, the wrapped phase image is unwrapped using a path tracking method. The pixels in the wrapped phase image are evaluated for phase quality and sorted according to the quality evaluation results. Image regions with higher quality values are prioritized for unwrapping. By unwrapping the wrapped phase region by region, the true absolute phase of each pixel in the wrapped phase image is obtained. The true absolute phase can reflect the true wrapped phase condition with uneven phase differences, laying the foundation for phase compensation and calibration.

[0064] Based on the obtained true absolute phases of different pixels, in step S103, phase compensation is performed on the first interference image to correct any phase distortion that may exist in the image, eliminate any non-uniformity in the phase distribution, regularize the interference fringes, and generate an interference image with a uniform phase distribution, providing data for subsequent topography restoration. After regenerating the uniform interference image, in step S104, the interference curves of each pixel are extracted from the uniform interference image. A certain number of interference curves are selected as a reference distribution, and the statistical differences between the remaining curves and the reference distribution are calculated. Interference curves with the same or similar curve distribution as the reference distribution are screened, thereby performing image restoration to obtain the surface topography of the object under test, achieving high-precision detection of the surface of tiny devices.

[0065] The second interference image is phase analyzed by principal component analysis to obtain a wrapped phase map including the wrapped phases of different pixel points of the second interference image. The wrapped phase map is then phase unwrapped by the path tracking method to obtain the true absolute phase of the pixel point. The phase of the first interference image is then compensated to correct the measurement error and improve the measurement accuracy and stability of the Michelson interferometer.

[0066] As an optional implementation, such as Figure 3 As shown, in step S101, the processing module performs phase analysis on the second interference image by principal component analysis to obtain a wrapped phase map, and further includes the following steps:

[0067] Step S201 : constructing an original data matrix based on a plurality of second interference images acquired by a second image acquisition system.

[0068] Step S202 : subtracting the background light intensity from the original data matrix to obtain the AC component matrix of the interference fringes.

[0069] Step S203: performing singular value decomposition on the AC component matrix.

[0070] Step S204 , performing principal component selection based on the singular value decomposition result, selecting the residual of background light intensity as the first principal component, the spatial distribution of the cosine component of the phase information as the second principal component, and the spatial distribution of the sine component of the phase information as the third principal component.

[0071] Step S205 , vectorizing the selected principal components, and obtaining a wrapped phase map based on the vectorization result.

[0072] Specifically, in step S201, a data matrix is constructed based on multiple second interference images captured by the second image acquisition system. For example, the piezoelectric ceramic moves from top to bottom, and the second image acquisition system captures and captures a total of 125 second interference images. These 125 second interference images are stacked to form an original data matrix. In this embodiment of the present application, the original data matrix is expressed as follows:

[0073] (1);

[0074] Wherein, D represents the original data matrix, R represents the real number set, and M represents the number of pixels of the interference image. In the embodiment of the present application, the number of pixels M is 758016.

[0075] After the original data matrix is constructed, in step S202, the background light intensity is subtracted from the original data matrix to separate the effective information including the interference fringes from the original data matrix to obtain the AC component matrix. In the embodiment of the present application, the expression of the AC component matrix is as follows:

[0076] (2);

[0077] Where D represents the original data matrix; Represents the background light intensity, and D0 represents the AC component matrix.

[0078] After obtaining the AC component matrix, in step S203, the AC component matrix is subjected to singular value decomposition, which decomposes the AC component matrix into the product of three matrices, decomposing the complex interference signal into independent principal components, providing a mathematical basis for phase information separation. The expression for singular value decomposition of the AC component matrix is as follows:

[0079] (3);

[0080] Wherein, U represents the left singular vector matrix, and the spatial pattern of the left singular vector matrix U is column vector orthogonal, that is, the characteristic distribution of the interference image; S represents the diagonal matrix, and the diagonal matrix S is used to reflect the energy distribution. The diagonal elements are singular values, and the diagonal elements of the diagonal matrix S can reflect the energy; V represents the right singular vector matrix, and the time pattern of the right singular vector matrix V is column vector orthogonal, and the column vectors of the right singular vector matrix V represent the evolution during the phase shift process.

[0081] Based on the singular value decomposition of the AC component matrix, in step S204, principal components are selected according to the decomposition results, wherein the residual of the background light intensity is selected as the first principal component, the spatial distribution of the cosine component of the phase information is selected as the second principal component, and the spatial distribution of the sine component of the phase information is selected as the third principal component.

[0082] After the principal components are selected, in step S205, the selected principal components are vectorized. The first principal component is the residual of the background light intensity, and its singular value is close to 0. The actual contribution of the first principal component can be ignored, so there is no need to vectorize the first principal component. The second and third principal components are vectorized, and the vectorization expressions are as follows:

[0083] (4);

[0084] Where, represents the spatial distribution of the second principal component U2, represents the spatial distribution of the third principal component U3, and vec represents vectorization.

[0085] For example, a matrix is expanded into a column vector in column-first order to facilitate efficient data processing in phase calculation, for example:

[0086] (5);

[0087] Where, Represents the spatial distribution of the second principal component U2.

[0088] The second principal component and the third principal component matrices are expanded into column vectors by rows through vectorization processing. Each column vector of the second principal component and the third principal component corresponds to the phase cosine and sine values of each pixel point respectively. The phase value of each pixel point is calculated by the inverse tangent function to obtain a wrapped phase map. Each pixel value in the wrapped phase map represents the phase information of the corresponding position. The wrapped phase situation with uneven phase difference is reflected by the phase information of each pixel point. Furthermore, when the Michelson interferometer plane mirror moves toward the light source so that the optical path difference is reduced, a negative sign is introduced into the inverse tangent function to compensate for the phase value. In an embodiment of the present application, the expression of the inverse tangent function is as follows:

[0089] (6);

[0090] Where, represents the wrapped phase, U2 represents the second principal component, and U3 represents the third principal component.

[0091] The second interference image is subjected to phase analysis using the principal component analysis method mentioned above, completing the conversion from the second interference image data to the wrapped phase map. The wrapped phase map reflects the phase jump caused by the nonlinearity of the actual displacement of the piezoelectric ceramic, providing key data for subsequent phase unwrapping and morphology restoration.

[0092] As an optional implementation, such as Figure 4 As shown, in step S102, the processing module performs phase unwrapping on the wrapped phase image by a path tracking method to obtain the true absolute phase of different pixel points, and further includes the following steps:

[0093] Step S301 : performing a quality assessment on the availability of pixels in the wrapped phase image, obtaining quality factors of pixels in different regions of the wrapped phase image, and generating a quality map based on the quality factors.

[0094] Step S302 : constructing a priority queue for different regions of the wrapped phase image based on the quality factor, and iteratively unwrapping regions with higher priority based on the priority queue to obtain the true absolute phase of each pixel in different regions.

[0095] Specifically, based on the wrapped phase image, the quality of the pixel availability in the wrapped phase image is evaluated, a quality factor is assigned to each pixel in the wrapped phase image, and the variance of the phase gradient is calculated in the local area. The smaller the variance, the smoother the phase change in the area, the smaller the noise interference, and the higher the quality factor. The expression for calculating the phase gradient variance is as follows:

[0096] (7);

[0097] Where, represents the gradient variance; represents the phase gradient; W represents the local area. In the embodiment of the present application, the local area W is 25*25; It represents the mean gradient in the local area W, which is used as a reference to measure the degree of deviation of each pixel.

[0098] Furthermore, the phase gradient Divided into horizontal gradient and vertical gradient .

[0099] Horizontal gradient The expression is as follows:

[0100] (8);

[0101] Where, Represents the phase value of pixel (i, j+1), Represents the phase value of pixel (i, j), where pixel (i, j+1) is the right neighboring pixel of pixel (i, j) in the matrix.

[0102] Vertical gradient The expression is as follows:

[0103] (9);

[0104] Where, Represents the phase value of pixel (i+1, j), Represents the phase value of pixel (i, j), where pixel (i+1, j) is the lower neighboring pixel of pixel (i, j) in the matrix.

[0105] By calculating the gradient amplitude in formula (7) , which can reflect the change in the gradient amplitude in the local area and judge whether there is data jump or noise influence. For example, when detecting the end face of the optical fiber connector, there is a distance between the optical fiber ferrule and the connector end face, where a phase jump may occur; or due to the presence of water, dust, oil stains and other noise interference points on the connector end face that are inconsistent with the end face material, a phase change may be found. In the embodiment of the present application, the gradient amplitude The calculation expression is as follows:

[0106] (10);

[0107] Where, represents the gradient amplitude, represents the horizontal gradient, Represents the vertical gradient.

[0108] The quality factor of the pixel is calculated by phase gradient variance, thereby generating a quality map. In the embodiment of the present application, the calculation expression of the quality factor is as follows:

[0109] (11);

[0110] Where, represents the quality factor; It is a minimum value of the order of 1 / 1000000. Used to protect the denominator from being zero to increase the reliability and stability of the data.

[0111] After obtaining the quality factors of pixels in different regions of the wrapped phase image, a priority queue is constructed based on the quality factors. According to the priority queue, regions with smaller phase gradient variances have higher quality values and are prioritized for unwrapping to obtain the true absolute phase of each pixel in each region. During the unwrapping process, starting from pixels in high-quality regions, the phase difference between adjacent pixels is calculated point by point. By adding correction terms that are integer multiples of 2π, the wrapped phase is unwrapped into a continuous true absolute phase. This process prioritizes regions with high reliability and gradually expands to lower-quality regions, ultimately obtaining the true absolute phase of the entire wrapped phase image. This effectively addresses the susceptibility of traditional path tracking methods to noise and improves the stability and accuracy of phase unwrapping.

[0112] In the embodiment of the present application, the expression of the true absolute phase is as follows:

[0113] (12);

[0114] Where, Represents the true absolute phase of the pixel point (x, y) obtained by unwrapping; Represents the wrapped phase value of the pixel (x, y) before unwrapping; k is an integer, and .

[0115] The value of k is chosen so that the phase is between -π and π. The calculation formula for integer k is:

[0116] (13);

[0117] Where, Indicates the unwrapped reference pixel, pixel point The neighboring pixels of the previously processed pixel (x, y) serve as a known quantity guide Unpacking; Indicates the wrapped phase value of the pixel (x, y), the range is [-π, π] or [0, 2π]; Represents pixel points The wrapped phase value, pixel is the neighborhood pixel of the pixel point (x, y).

[0118] According to the priority queue, iteratively unwrap the areas with higher priority first, and set the unwrapping along the path within the area to obtain the true absolute phase of each pixel in different areas. The phase needs to meet the following requirements:

[0119] (14);

[0120] Where, Indicates the true absolute phase; represents the unwrapped reference phase; Indicates the wrapped phase value of the pixel (x, y); Indicates the wrapped phase value of the neighborhood pixels of the pixel point (x, y).

[0121] Furthermore, as an optional implementation, the processing module is configured to: when performing phase unwrapping on the wrapped phase image, if the height and phase relationship of the object to be measured satisfies:

[0122] (15);

[0123] Where λ represents the wavelength of the second light source, h(x, y) represents the height of the object to be measured at the coordinate (x, y), Indicates the true absolute phase of the pixel (x, y).

[0124] A curvature constraint is added to the height of the object to be measured, limiting the second-order derivative of the height of the surface of the object to be measured to avoid severe phase oscillation caused by noise or abnormal data. The curvature constraint is expressed by the following formula:

[0125] (16);

[0126] Where k represents the curvature constraint, h represents the height of the pixel, x represents the horizontal coordinate value of the pixel, and y represents the vertical coordinate value of the pixel.

[0127] By combining the priority and curvature constraints of the quality map, the wrapped phase is gradually converted into the true absolute phase reflecting the actual optical path difference, accurately reflecting the actual displacement phase of the calibration system and providing precise calibration parameters for subsequent phase compensation.

[0128] As an optional implementation, such as Figure 5 As shown, in step S103, the processing module performs phase compensation on the first interference image in the first Michelson interference optical cable based on the true absolute phase to regenerate a uniform interference image, and further includes the following steps:

[0129] Step S401: Calculate the phase compensation value of each pixel point according to the true absolute phase of each pixel point using the following formula:

[0130] (17);

[0131] Where, is the standard displacement of the piezoelectric ceramic controller, and , is the actual displacement of the piezoelectric ceramic, λ is the wavelength of the second light source, Indicates the true absolute phase of the pixel, Indicates the phase compensation value.

[0132] During the phase compensation process, the displacement amount manually set by the piezoelectric ceramic controller is used as the standard amount. The actual displacement amount is not fixed and is reflected by the uneven phase difference. Therefore, the phase compensation value can be obtained by subtracting the standard displacement amount from the true absolute phase of the pixel point. In addition, the displacement directions of the first Michelson interferometer optical path and the second Michelson interferometer optical path are opposite, and thus the phase compensation presents an opposite numerical relationship. By calculating the phase compensation value of each pixel point, phase compensation is performed on each pixel point to eliminate the phase error of the pixel point.

[0133] Step S402 performs phase compensation on the pixel points at corresponding coordinates in the first interference image based on the phase compensation value, thereby regenerating a uniform interference image. Specifically, the wavelengths of the light sources of the first Michelson interferometer optical path and the second Michelson interferometer optical path differ, resulting in an uncorrected phase extracted from the envelope of the first Michelson interferometer optical path. In the phase compensation calculation for the pixel points at corresponding coordinates in the first interference image, the error in the envelope extraction caused by the phase offset and the phase compensation value are introduced, thereby updating the phase parameters of the modulation amplitude of the first Michelson interferometer optical path and regenerating the uniform interference image.

[0134] As an optional implementation, the processing module performs phase compensation on the pixel points of corresponding coordinates in the first interference image using the following formula:

[0135] (18);

[0136] Where, Indicates the grayscale value of the pixel after compensation, represents the DC component of the background light intensity in the first Michelson interference optical path, represents the modulation amplitude of the first Michelson interference optical path, represents the uncompensated gray value of the first interference image pixel, Indicates the standard displacement of the piezoelectric ceramic controller.

[0137] As an optional implementation, such as Figure 6 As shown, in step S104, the processing module performs image restoration based on the regenerated uniform interference image to obtain the surface morphology of the object to be measured, and further includes the following steps:

[0138] Step S501 : generating interference curves of different pixel points based on corresponding pixel points in a plurality of uniform interference images.

[0139] Step S502 : Select some of the interference curves as normal interference curves, and generate a reference distribution based on the selected normal interference curves.

[0140] In step S503 , a two-sample normality test is used to screen interference curves whose curve distribution is the same or similar to the reference distribution from the remaining interference curves, generate a new data set, and perform image restoration based on the new data set to obtain the surface morphology of the object to be measured.

[0141] Specifically, in step S501, multiple uniform interference images are analyzed, and the grayscale value sequence of each pixel point is extracted from the regenerated uniform interference image to generate interference curves of different pixel points. The interference curve can reflect the grayscale modulation caused by the change of optical path difference during the displacement of the piezoelectric ceramic, and the peak of its envelope corresponds to the position of zero optical path difference. For example, the resolution of the uniform interference image is 1344*564, with a total of 758016 pixels, and there are 758016 interference curves. For example, the interference curve of a normal pixel point is as follows Figure 7 As shown, the interference curve of the noise pixel point is as follows Figure 8 As shown in the figure, the horizontal axis represents the moving distance and the vertical axis represents the grayscale value.

[0142] After generating interference curves of different pixel points, in step S502, areas with clear interference fringes, high contrast and no obvious noise are selected, and the interference curves corresponding to these areas are extracted as normal interference curves. A reference distribution is generated based on the selected normal interference curves. For example, 1000 interference fringes are selected from 758016 interference curves as normal interference curves, and the remaining 757016 interference curves are used as test curves. The actual light intensity value of the normal interference curve is set to , where (j=1,2,3…1000), Gaussian fitting is performed on 1000 normal interference curves to obtain the predicted model light intensity value , the quadratic Gaussian function fits the interference curve as Figure 9 As shown, the maximum point of the envelope is the position of zero optical path difference. The residual of the actual light intensity value of the normal interference curve and the light intensity value of the predicted model is calculated as follows:

[0143] (19);

[0144] Where, Indicates the actual light intensity value of the normal interference curve, represents the predicted model light intensity value, Represents the residual.

[0145] Mix 1000 normal interference curves with 125 data points on each curve into a large set As a reference residual distribution set, the capacity of the reference residual distribution set is 1000*125=125000. Further, all data are sorted from small to large to generate a reference distribution. The expression of the reference distribution is as follows:

[0146] (20);

[0147] Where, represents the reference distribution, represents the reference residual distribution set The i-th sample in , I Indicates the light intensity value.

[0148] The remaining 757,016 curves to be tested were preprocessed using a two-sample state test. The residuals of the curves to be tested were calculated. The two-sample state test method was used to filter out normal pixels from the noise pixels and normal pixels for feature extraction. This significantly reduced the amount of data required for calculation, thereby increasing the speed of data analysis. The residual calculation expression for the Kth curve to be tested is as follows:

[0149] (twenty one);

[0150] Where, Indicates the actual light intensity value of the Kth curve to be measured, Indicates the model light intensity value of the Kth curve to be measured.

[0151] Establish a set based on the residual of the Kth curve to be tested , the capacity of the set is 125. The empirical distribution function expression of the Kth curve to be tested is:

[0152] (twenty two);

[0153] Where, Representing a collection The rth sample in .

[0154] The residual set of the Kth curve to be tested and the reference residual distribution set The two-sample state test statistic is calculated, and its calculation expression is as follows:

[0155] (twenty three);

[0156] In the formula, Z is the number of duplicate values removed. The value sorting set; n1 is the reference residual distribution set The capacity of n1 is 125000; n2 is the residual set The capacity of , and n2 is 125; W 2 represents the two-sample status test statistic.

[0157] The significance of the remaining interference curves is judged, and the null hypothesis H0 is set: the distribution of the interference curve to be tested is similar to or the same as the reference distribution, and it is a normal pixel point; the alternative hypothesis H1 is: the curve to be tested is significantly different from the reference distribution, and it is a noise interference curve. The significance of the interference curve to be tested is judged, and the significance level α = 0.05 is set. The statistical critical value is generated by Monte Carlo simulation or table lookup. .

[0158] If the two-sample state test statistic W 2 Greater than or equal to the critical value of the statistic , reject the original hypothesis H0, that is, the current curve is significantly different from the reference distribution and is the interference curve of the noise pixel point; on the contrary, if the two-sample state test statistic W 2 Less than the critical value of the statistic , accept the null hypothesis H0, that is, the current curve is similar or identical to the reference distribution and is the interference curve of normal noise points. Based on the interference curve that is identical or similar to the reference distribution, a new data set is generated. The topography restoration analysis is performed on this data set to finally obtain the surface topography of the object to be measured.

[0159] According to the above description, the present application provides a Michelson interferometer, which ensures that the displacement of the first Michelson interferometer as a measurement system and the second Michelson interferometer as a calibration system are synchronized by sharing the same piezoelectric ceramic through the first Michelson interferometer optical path and the second Michelson interferometer optical path, so that the phase change of the second interference image obtained by the second Michelson interferometer optical path can accurately reflect the actual phase data of the first Michelson interferometer optical path; the second interference image is phase analyzed by the principal component analysis method to obtain a wrapped phase map including the wrapped phases of different pixel points of the second interference image, and the wrapped phase map is phase unwrapped by the path tracking method to obtain the true absolute phase of the pixel point, and then the phase of the first interference image is compensated, the measurement error is corrected, and the image is restored based on the corrected first interference image, and finally the accurate surface morphology of the object to be measured is obtained, and real-time data feedback and error calibration are realized during the detection process, thereby improving the accuracy and reliability of the morphology detection of micro devices.

[0160] In a second aspect, the present application also provides a method for detecting the morphology of a micro device, which is applied to the Michelson interferometer described above, such as Figure 10 As shown, the method includes the following steps:

[0161] Step S601: perform phase analysis on the second interference image by principal component analysis to obtain a wrapped phase map, which includes the wrapped phases of different pixel points of the second interference image, and perform phase unwrapping on the wrapped phase map by path tracking to obtain the true absolute phases of different pixel points.

[0162] Step S602 : performing phase compensation on the first interference image based on the true absolute phase, regenerating a uniform interference image, and performing image restoration based on the regenerated uniform interference image to obtain the surface topography of the object to be measured.

[0163] This method for detecting the morphology of a tiny device performs phase analysis on the second interference image using a principal component analysis method to obtain a wrapped phase map including the wrapped phases of different pixel points in the second interference image, and performs phase unwrapping on the wrapped phase map using a path tracking method to obtain the true absolute phase of the pixel point. The phase of the first interference image is then compensated to correct the measurement error, and image restoration is performed based on the corrected first interference image to ultimately obtain the accurate surface morphology of the object to be measured, thereby realizing real-time data feedback and error calibration during the detection process, and improving the accuracy and reliability of tiny device morphology detection.

[0164] It should be noted that the micro-device morphology detection method is applied to the Michelson interferometer described above, so the specific limitations in the embodiment of the micro-device morphology detection method can refer to the above limitations on the Michelson interferometer and will not be repeated here.

[0165] It will be understood that the word "exemplary" as used herein means "serving as an example, instance or illustration". Any embodiment described as "exemplary" is not necessarily preferred or superior to other embodiments and / or does not exclude the combination of features of other embodiments. It will be understood that certain features of the present application described in the context of separate embodiments for the sake of clarity may also be provided in a single embodiment by combination. Conversely, various features of the present application described in the context of a single embodiment for the sake of clarity may also be provided individually or in any suitable combination or as any other described embodiment of the present application. In addition, "at least one" means one or more, and "a plurality of" means two or more. Words such as "first" and "second" do not limit the quantity and order of execution, and words such as "first" and "second" do not limit them to be necessarily different.

[0166] The above disclosure is only a preferred embodiment of the present application, but it is not intended to limit the scope of rights of the present application. A person skilled in the art can understand that without departing from the spirit and scope of the present application and the appended claims, changes, modifications, substitutions, combinations, and simplifications should all be equivalent replacement methods and still fall within the scope of the invention.

Claims

1. A Michelson interferometer, characterized in that The Michelson interferometer comprises: A first Michelson interferometer optical path includes a first light source, a workbench, a first beam splitter, a first test reflector, and a first image acquisition system. The workbench is used to place an object to be measured. The light beam emitted by the first light source is split by the first beam splitter. One beam is reflected onto the surface of the object to be measured, and the other beam is transmitted to the first test reflector. The two beams are reflected by the object to be measured and the first test reflector respectively and return, interfering at the first beam splitter. The first image acquisition system receives a first interference image. A second Michelson interferometer optical path includes a second light source, a calibration reflector, a second beam splitter, a second test reflector, and a second image acquisition system. The light beam emitted by the second light source is split by the second beam splitter, one beam is reflected onto the surface of the calibration reflector, and the other beam is transmitted to the second test reflector. The two beams are reflected by the calibration reflector and the second test reflector respectively and return, interfering at the second beam splitter. The second image acquisition system receives a second interference image. The first Michelson interference optical path and the second Michelson interference optical path share the same piezoelectric ceramic, and the piezoelectric ceramic is configured to control the displacement of the first test reflector and the second test reflector.

2. The Michelson interferometer according to claim 1, wherein The second light source is configured as a helium-neon laser to eliminate dispersion effects in the second Michelson interference optical path; The Michelson interferometer further includes a processing module configured to perform phase analysis on the second interference image by a principal component analysis method to obtain a wrapped phase map, wherein the wrapped phase map includes the wrapped phases of different pixels of the second interference image, and perform phase unwrapping on the wrapped phase map by a path tracking method to obtain true absolute phases of different pixels; The processing module performs phase compensation on the first interference image based on the true absolute phase, regenerates a uniform interference image, and performs image restoration based on the regenerated uniform interference image to obtain the surface morphology of the object to be measured.

3. The Michelson interferometer according to claim 2, wherein: The processing module performing phase analysis on the second interference image by using a principal component analysis method includes: constructing an original data matrix based on the plurality of second interference images acquired by the second image acquisition system; Subtracting the background light intensity from the original data matrix to obtain the AC component matrix of the interference fringes; Perform singular value decomposition on the AC component matrix, The principal components are selected based on the singular value decomposition results. The residual of the background light intensity is selected as the first principal component, the spatial distribution of the cosine component of the phase information is selected as the second principal component, and the spatial distribution of the sine component of the phase information is selected as the third principal component. The selected principal components are vectorized, and the wrapped phase map is obtained based on the vectorization result.

4. The Michelson interferometer according to claim 3, wherein The processing module performs phase unwrapping on the wrapped phase image by a path tracking method, comprising: Performing a quality assessment on the availability of pixels in the wrapped phase image, obtaining quality factors of pixels in different regions of the wrapped phase image, and generating a quality map based on the quality factors; A priority queue of different regions of the wrapped phase image is constructed based on the quality factor. According to the priority queue, regions with higher priority are iteratively unwrapped to obtain the true absolute phase of each pixel point in different regions.

5. The Michelson interferometer according to claim 4, wherein: The processing module is further configured to, when performing phase unwrapping, if the height and phase relationship of the object to be measured satisfies: , then add a curvature constraint to the height of the object to be measured, and the curvature constraint is expressed by the following formula: ； Where λ represents the wavelength of the second light source, h ( x , y ) represents the coordinates ( x , y ) at the height of the object to be measured, Represents a pixel ( x , y )’s true absolute phase, k Represents a curvature constraint.

6. The Michelson interferometer according to claim 4, wherein The processing module performs phase compensation on the first interference image in the first Michelson interference optical path based on the true absolute phase to regenerate a uniform interference image, including: According to the true absolute phase of each pixel, the phase compensation value of different pixels is calculated by the following formula: ； Where, is the standard displacement of the piezoelectric ceramic controller, , is the actual displacement of the piezoelectric ceramic, λ represents the wavelength of the second light source, Indicates the true absolute phase of the pixel, Based on the phase compensation value, phase compensation is performed on the pixel points of corresponding coordinates in the first interference image to regenerate a uniform interference image.

7. The Michelson interferometer according to claim 6, wherein The processing module performs phase compensation on the pixel points of corresponding coordinates in the first interference image using the following formula: ； Where, Indicates the grayscale value of the pixel after compensation, represents the DC component of the background light intensity in the first Michelson interference optical path, represents the modulation amplitude of the first Michelson interference optical path, represents the uncompensated gray value of the first interference image pixel, Indicates the standard displacement of the piezoelectric ceramic controller.

8. The Michelson interferometer according to claim 7, wherein: The processing module is further configured to: generate interference curves of different pixel points based on the corresponding pixel points in the plurality of uniform interference images, Selecting some of the interference curves as normal interference curves, and generating a reference distribution based on the selected normal interference curves; A two-sample normality test is used to screen interference curves whose curve distribution is the same or similar to the reference distribution from the remaining interference curves to generate a new data set. Image restoration is performed based on the new data set to obtain the surface morphology of the object to be measured.

9. The Michelson interferometer according to claim 1, wherein The first light source is configured to provide white light.

10. A method for detecting the morphology of a micro device, characterized in that: The method uses the Michelson interferometer according to any one of claims 1 to 9, and the method comprises the following steps: performing phase analysis on the second interference image by a principal component analysis method to obtain a wrapped phase map, wherein the wrapped phase map includes the wrapped phases of different pixels of the second interference image, and performing phase unwrapping on the wrapped phase map by a path tracing method to obtain true absolute phases of different pixels; Based on the true absolute phase, phase compensation is performed on the first interference image to regenerate a uniform interference image, and image restoration is performed based on the regenerated uniform interference image to obtain the surface morphology of the object to be measured.

Images