Focusing and leveling measurement method and measurement system

Abstract

The present disclosure provides a focusing and leveling measurement method and measurement system, which include: imaging an optical grating on the surface of a measured object through light beam illumination to form an optical grating pattern, which is further reflected onto an imaging plane of an optical sensor; encoding pixel points on the optical sensor to maintain or clear light intensity signals at the pixel points to form a digital grating pattern; the digital grating and the optical grating have the same duty cycle, and a preset difference between their periods; forming a synthetic grating pattern by overlapping the optical grating pattern and the digital grating pattern; after measurement, performing light intensity integration on the synthetic grating pattern to determine the displacement of the optical grating pattern on the imaging plane; and determining the height of the measured object surface based on a linear relationship between the displacement and the height of the measured object surface. Compared with the existing technology, the focusing and leveling measurement speed and accuracy can be improved, and the complexity of the measurement system can be reduced.

Description

Technical Field

[0001] The present disclosure relates to the technical field of focusing and leveling, and in particular to a focusing and leveling measurement method and measurement system. Background Art

[0002] With the rapid development of microelectronics and the continuous improvement of extreme ultraviolet lithography, the critical dimensions of very large-scale integrated circuits have entered the nanometer era. To achieve higher resolution, the industry must sacrifice focal depth. During the lithography exposure process, factors such as wafer surface topography fluctuations, photoresist thickness variations, and deviations in the projection lens focal plane can cause the wafer to defocus and tilt relative to the projection lens focal plane. When wafer defocus and tilt cause portions of the exposure field of view to exceed the depth of focus, the exposed image quality is severely affected.

[0003] Currently, the latest extreme ultraviolet (EUV) lithography systems require a depth of focus control range of only 60nm, a problem that has become a major obstacle to the development of lithography technology. Focus and leveling technology allows real-time adjustment of the position and posture of the wafer stage to keep the wafer surface within this control range. Therefore, developing a focus and leveling measurement system with nanometer-level precision is of great value and significance for ensuring the quality of patterns exposed by advanced lithography systems.

[0004] Accurate measurement of silicon wafer surface topography is the prerequisite for ensuring high-precision focusing and leveling measurement. There is currently a dual-stage focusing and leveling measurement system based on grating metrology, such as Figure 1 As shown, a white light source is introduced into an illumination system 112 via an optical fiber 111, collimating the light beam to uniformly illuminate a grating 113. The grating is then imaged onto a silicon wafer via a dual-telecentric imaging system 114. After reflection from the silicon wafer, the grating image on the silicon wafer is imaged onto a glued assembly of a polarizer 124, a spectroscopic crystal 125, and a grating 126 via a dual-telecentric system 121, forming a moiré fringe signal. The signal then reaches a detector 128 in a time-sharing manner via a spectroscopic system 127. Differential signal processing is used to obtain the surface height of the silicon wafer. The main drawback of this method is that the detection grating 126 requires bonding optical elements such as polarizers and beam shifters. Bonding optical elements can easily cause deformation of the elements, affecting imaging quality and further affecting measurement accuracy. At the same time, the subsequent spectroscopic optical system has strict requirements on polarization spectrometry performance, and the production of high-performance photodetectors is also difficult.

[0005] Another existing detection technology uses a charge-coupled device (CCD) sensor to detect silicon wafer surface topography. This technology divides the pixels on the CCD sensor into two groups based on odd and even rows. The output terminals of the odd and even pixel rows are hardware-connected to form a common output terminal, creating an alternating periodic structure on the CCD pixel array. A periodic projected grating and the CCD sensor work together to form moiré fringes. Light passing through the projected grating generates incident light with spatially periodic intensity variations. After reflection from the wafer surface, it is received by the CCD sensor. The changes in the reflected light intensity signal are used to reflect changes in the wafer surface topography height. For example, the average offset of the grating line intensity pattern can be used to determine the wafer surface height variation. This detection method using CCD sensors is widely used in modern industrial technology, such as computer vision, mechanical parts processing, and quality inspection. However, the resolution of measurement results derived solely from light intensity signal acquisition and simple calculations is greatly limited by the sensor itself, making it difficult to meet the ever-increasing measurement accuracy. In addition, the entire measurement process is usually divided into two parts: coarse measurement and fine measurement. Fine measurement and coarse measurement use completely different marking and measurement principles, which increases the complexity of the entire system. Summary of the Invention

[0006] The purpose of the present disclosure is to provide a focusing and leveling measurement method and a measurement system to improve the speed and accuracy of focusing and leveling measurement and reduce the complexity of the measurement system.

[0007] A first aspect of the present disclosure provides a focusing and leveling measurement method, the method comprising: imaging an optical grating on a surface of a measured object through light beam illumination to form an optical grating pattern, the optical grating pattern further reflected onto an imaging plane of an optical sensor;

[0008] Encoding the pixels on the optical sensor to maintain or clear the light intensity signal at the pixel, thereby forming a digital grating pattern; the digital grating has the same duty cycle as the optical grating, and there is a preset difference between their periods;

[0009] forming a composite grating pattern by overlapping the optical grating pattern with the digital grating pattern;

[0010] After measurement, performing light intensity integration on the synthetic grating pattern to determine the displacement of the optical grating pattern on the imaging plane;

[0011] The height of the surface of the object to be measured is determined according to a linear relationship between the displacement and the height of the surface of the object to be measured.

[0012] According to some embodiments of the present disclosure, forming a synthetic grating pattern by overlapping the optical grating pattern with the digital grating pattern includes:

[0013] Overlapping the optical grating pattern with the digital grating pattern to obtain a first synthetic grating pattern;

[0014] The digital grating pattern code is inverted and then overlapped with the optical grating pattern to obtain a second synthetic grating pattern.

[0015] According to some embodiments of the present disclosure, after the measurement, performing light intensity integration on the synthetic grating pattern to determine the displacement of the optical grating pattern on the imaging plane includes:

[0016] After measurement, performing light intensity integration on the first synthetic grating pattern to obtain a first light intensity position relationship curve;

[0017] After measurement, performing light intensity integration on the second synthetic grating pattern to obtain a second light intensity position relationship curve;

[0018] Normalizing the first light intensity position relationship curve and the second light intensity position relationship curve to obtain a normalized differential moiré fringe intensity curve;

[0019] Obtaining the phase of the differential moiré fringe intensity curve according to a preset phase extraction algorithm, and comparing the phase with a reference phase to obtain a phase change value;

[0020] The displacement is determined according to a linear relationship between the phase change value and the displacement of the optical grating pattern on the imaging plane.

[0021] According to some embodiments of the present disclosure, obtaining the phase of the differential moiré fringe intensity curve according to a preset phase extraction algorithm includes:

[0022] Performing a fast Fourier transform on the differential moiré fringe intensity curve to obtain a corresponding frequency spectrum;

[0023] Determining the modal decomposition level K value according to the number of harmonics contained in the spectrum;

[0024] According to the K value, performing a first variational mode decomposition on the differential moiré fringe intensity curve to obtain a series of intrinsic mode functions;

[0025] Performing a fast Fourier transform on each of the intrinsic mode functions to obtain a first fundamental wave signal;

[0026] Performing a second variational mode decomposition on the first fundamental wave signal to obtain a second fundamental wave signal after noise reduction;

[0027] Performing a Hilbert transform on the second fundamental wave signal to obtain the phase of the differential moiré fringe intensity curve.

[0028] According to some embodiments of the present disclosure, the number of signal decompositions of the second variational mode decomposition is set to 2.

[0029] A second aspect of the present disclosure provides a focusing and leveling measurement system, comprising:

[0030] A light source, used to generate the light beam required for measurement;

[0031] an optical grating located downstream of the light source; the optical grating is imaged on the surface of the object to be measured by the light beam to form an optical grating pattern; the optical grating pattern is further reflected onto an imaging plane of the optical sensor;

[0032] The optical sensor is configured to receive the optical grating pattern;

[0033] A data processing module is in communication with the optical sensor and is configured to implement the following steps:

[0034] Encoding the pixels on the optical sensor to maintain or clear the light intensity signal at the pixel, thereby forming a digital grating pattern; the digital grating has the same duty cycle as the optical grating, and there is a preset difference between their periods;

[0035] forming a composite grating pattern by overlapping the optical grating pattern with the digital grating pattern;

[0036] After measurement, performing light intensity integration on the synthetic grating pattern to determine the displacement of the optical grating pattern on the imaging plane;

[0037] The height of the surface of the object to be measured is determined according to a linear relationship between the displacement and the height of the surface of the object to be measured.

[0038] According to some embodiments of the present disclosure, the data processing module is specifically configured to:

[0039] Overlapping the optical grating pattern with the digital grating pattern to obtain a first synthetic grating pattern;

[0040] The digital grating pattern code is inverted and then overlapped with the optical grating pattern to obtain a second synthetic grating pattern.

[0041] According to some embodiments of the present disclosure, the data processing module is specifically configured to:

[0042] After measurement, performing light intensity integration on the first synthetic grating pattern to obtain a first light intensity position relationship curve;

[0043] After measurement, performing light intensity integration on the second synthetic grating pattern to obtain a second light intensity position relationship curve;

[0044] Normalizing the first light intensity position relationship curve and the second light intensity position relationship curve to obtain a normalized differential moiré fringe intensity curve;

[0045] Obtaining the phase of the differential moiré fringe intensity curve according to a preset phase extraction algorithm, and comparing the phase with a reference phase to obtain a phase change value;

[0046] The displacement is determined according to a linear relationship between the phase change value and the displacement of the optical grating pattern on the imaging plane.

[0047] According to some embodiments of the present disclosure, the data processing module is specifically configured to:

[0048] Performing a fast Fourier transform on the differential moiré fringe intensity curve to obtain a corresponding frequency spectrum;

[0049] Determining the modal decomposition level K value according to the number of harmonics contained in the spectrum;

[0050] According to the K value, performing a first variational mode decomposition on the differential moiré fringe intensity curve to obtain a series of intrinsic mode functions;

[0051] Performing a fast Fourier transform on each of the intrinsic mode functions to obtain a first fundamental wave signal;

[0052] Performing a second variational mode decomposition on the first fundamental wave signal to obtain a second fundamental wave signal after noise reduction;

[0053] Performing a Hilbert transform on the second fundamental wave signal to obtain the phase of the differential moiré fringe intensity curve.

[0054] According to some embodiments of the present disclosure, the number of signal decompositions of the second variational mode decomposition is set to 2.

[0055] The advantages of the present disclosure compared with the prior art are:

[0056] The present disclosure provides a focusing and leveling measurement method and measurement system. An optical grating is imaged on the surface of a measured object under light beam illumination to form an optical grating pattern. The optical grating pattern is further reflected onto an imaging plane of an optical sensor, and pixel points on the optical sensor are encoded to achieve the retention or removal of light intensity signals at the pixel points, thereby forming a digital grating pattern. The digital grating and the optical grating have the same duty cycle, and there is a preset difference between their periods. A synthetic grating pattern is formed by overlapping the optical grating pattern and the digital grating pattern. After measurement, the synthetic grating pattern is subjected to light intensity integration to determine the displacement of the optical grating pattern on the imaging plane. The height of the measured object surface is determined based on the linear relationship between the displacement and the height of the measured object surface. Compared with the existing technology, the focusing and leveling measurement speed and accuracy can be improved, and the complexity of the measurement system can be reduced. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Various other advantages and benefits will become apparent to those skilled in the art upon reading the detailed description of the preferred embodiment below. The accompanying drawings are for illustration purposes only and are not to be considered as limiting the present disclosure. The same reference symbols are used throughout the drawings to represent the same components. In the drawings:

[0058] Figure 1 A schematic diagram of an existing dual-stage focusing and leveling measurement system based on a projection grating method is shown;

[0059] Figure 2 A schematic diagram of a focusing and leveling measurement system provided by the present disclosure is shown;

[0060] Figure 3 A flow chart of a focusing and leveling measurement method provided by the present disclosure is shown;

[0061] Figure 4a shows an overlay of an optical grating pattern and two complementary digital grating patterns;

[0062] Figure 4b A composite grating pattern of an optical grating pattern and a digital grating pattern is shown;

[0063] Figure 5 shows a flow chart of step S103 provided by the present disclosure;

[0064] Figure 6a The integrated light intensity curves I1 and I2 are shown;

[0065] Figure 6b For Figure 6a The corresponding normalized light intensity curve I;

[0066] Figure 7 The normalized light intensity curve I in actual measurement is shown;

[0067] Figure 8 shows a flow chart of step S204 provided by the present disclosure;

[0068] Figure 9 The time domain waveform of the simulated light intensity curve I signal is shown;

[0069] Figure 10 The frequency domain waveform of the simulated light intensity curve I signal is shown;

[0070] Figure 11 The time domain waveforms of the eigenmode functions obtained by the first variational mode decomposition are shown;

[0071] Figure 12 The frequency domain waveforms of the eigenmode functions obtained by the first variational mode decomposition are shown;

[0072] Figure 13 The time domain waveforms of the eigenmode functions obtained by the second variational mode decomposition are shown;

[0073] Figure 14 The figure shows the comparison of the original signal, fundamental IMF signal and fundamental signal frequency waveform of the moiré fringe;

[0074] Figure 15 The time domain waveforms of the eigenmode functions obtained by the first variational mode decomposition after adjusting the noise component are shown. DETAILED DESCRIPTION

[0075] Hereinafter, embodiments of the present disclosure will be described with reference to the accompanying drawings. However, it should be understood that these descriptions are merely illustrative and are not intended to limit the scope of the present disclosure. In addition, in the following description, descriptions of well-known structures and technologies are omitted to avoid unnecessary confusion of the concepts of the present disclosure.

[0076] The accompanying drawings illustrate various schematic diagrams of structures according to embodiments of the present disclosure. These figures are not drawn to scale, and for the purpose of clarity, certain details are exaggerated and certain details may be omitted. The shapes of the various regions and layers shown in the figures, as well as their relative sizes and positional relationships, are merely exemplary and may deviate in practice due to manufacturing tolerances or technical limitations. Those skilled in the art may design regions / layers with different shapes, sizes, and relative positions as needed.

[0077] It should be noted that the terms "object," "object to be measured," or "tested object" in this document refer to any physical object with specular features or specular reflective properties. For example, the test object may include a silicon wafer, a mirror, or a glass product.

[0078] The present application proposes a focusing and leveling measurement method and measurement system, which encodes an optical sensor such as a charge coupled device (CCD) or a complementary metal oxide semiconductor (CMOS) to replace the detection grating in the classical grating metrology method. This grating is hereinafter referred to as a digital grating. A light beam from a light source is projected onto the surface of the object to be measured through an optical grating, and then reflected onto the imaging plane of the optical sensor to form an image of the optical grating. Two digital gratings that are complementary in digital encoding are set, and two moiré fringe patterns are formed by overlapping the optical grating pattern and the digital grating pattern and pixelating them. Two light intensity curves containing the height information of the object to be measured are obtained by integrating the moiré fringe patterns. A normalized light intensity difference curve is constructed based on the two light intensity curves. The phase change of the normalized light intensity difference curve can directly reflect the height change of the object to be measured. The height of the object to be measured can be accurately calculated using a phase extraction algorithm based on variational mode decomposition and fast Fourier transform.

[0079] The following is a description with reference to the accompanying drawings.

[0080] Figure 2 This is an example of the focusing and leveling measurement system provided in this application being used for silicon wafer height measurement. After a light beam 204 emitted by a light source (which can be a polarized or unpolarized laser light source or an LED light source) passes through an optical grating 201 with a period of (P + ΔP), the outgoing light carrying the optical grating pattern information is reflected from the surface of a silicon wafer 202 and received by an optical sensor 203. In this application, software is used to encode a fringe pattern with a period of P on the optical sensor. The period difference between the optical grating and the fringe pattern on the optical sensor is set to a certain value, ΔP. As a result, the optical sensor receives a light signal with an intensity that varies periodically in space. When silicon wafer 202 moves h vertically relative to a reference plane, the optical grating pattern moves D horizontally on optical sensor 203. Based on the mirror reflection properties of the silicon wafer, the quantitative relationship between h and D is:

[0081]

[0082] Where α is the angle between the incident light beam and the silicon wafer, and M is the magnification of the detection optical system. After the device is installed and adjusted, the angle α between the incident light beam and the optical system magnification M is assumed to be constant. The vertical movement h is linearly related to the horizontal displacement D of the optical grating pattern on the optical sensor 203.

[0083] It should be noted that other optical elements, such as one or more lenses, may be disposed along the optical path between the optical grating 201 and the silicon chip 202 .

[0084] Figure 3A flow chart of a focusing and leveling measurement method provided by the present disclosure is shown; the method is applied to Figure 2 In the focusing and leveling measurement system shown, an optical grating is imaged on the surface of the object to be measured by light beam illumination to form an optical grating pattern, and the optical grating pattern is further reflected onto the imaging plane of the optical sensor.

[0085] like Figure 3 As shown, the focusing and leveling measurement method provided by the present disclosure includes the following steps S101 to S104:

[0086] Step S101: Encoding pixels on the optical sensor to maintain or clear light intensity signals at the pixels, thereby forming a digital grating pattern; the digital grating and the optical grating have the same duty cycle, and there is a preset difference between their periods;

[0087] Specifically, the duty cycle of the optical grating can be 1:1, and the grating fringe signal is a periodic light intensity distribution pattern in space with a period of (P+ΔP). Similarly, in an embodiment of the present disclosure, a digital grating with a duty cycle of 1:1 and a digital grating pattern with a period of P is set, and the value of the period difference ΔP between the two can be positive or negative. For example, the period difference ΔP between the period P+ΔP of the optical grating and the period P of the digital grating is less than or equal to half of the period P. Furthermore, the period difference ΔP between the optical grating and the digital grating determines the measurement resolution of the focusing and leveling measurement system. As a result, the measurement resolution can reach a very small proportion of a pixel (for example, 1 / 40 pixel).

[0088] Step S102: forming a synthetic grating pattern by overlapping the optical grating pattern and the digital grating pattern;

[0089] According to some embodiments of the present disclosure, step S102 specifically includes: overlapping the optical grating pattern and the digital grating pattern to obtain a first synthetic grating pattern; and inverting the digital grating pattern code and overlapping it with the optical grating pattern to obtain a second synthetic grating pattern.

[0090] Specifically, the digital grating is essentially a digital filter. By encoding 1 and 0 on the optical sensor, it can maintain (encode 1) or clear (encode 0) the light intensity signal at the pixel point. Note that in the above steps, two complementary digital gratings will be generated (digital gratings before and after encoding inversion). The mathematical models of the optical grating image and the complementary digital grating can be represented by the encoding matrices A, B, and Characterization:

[0091]

[0092] Among them, the matrix element subscript r is the number of pixel rows of the optical sensor, and c is the number of pixel columns of the optical sensor. By selecting a suitable digital grating period, the light intensity signal waveform of the entire period can be obtained after signal processing.

[0093] Figure 4a The pattern of the optical grating overlapped with the digital grating with a period of 4 pixels is shown. The digital grating is encoded to generate two complementary digital gratings B and Digital raster B is white area kept (code 1), gray area cleared (code 0); The white area is cleared (coded 0) and the gray area is retained (coded 1) (the specific setting method of the digital grating adopts relevant technology and is not described here). When the optical grating image is superimposed on the two digital grating images, two new complementary patterns are formed, which are referred to as the first synthetic grating pattern and the second synthetic grating pattern. The superposition process is mathematically the multiplication of the elements at the corresponding positions of the matrix, as shown below:

[0094] C1=A*B (2)

[0095]

[0096] C1+C2=A (4)

[0097] After the optical grating pattern and the mathematical grating pattern are overlapped, Figure 4b The middle left picture is the first synthetic grating pattern. Figure 4b The middle right image shows the second synthetic grating pattern.

[0098] Step S103: performing light intensity integration on the synthetic grating pattern after measurement to determine the displacement of the optical grating pattern on the imaging plane;

[0099] In this application, a digital grating is constructed using software to generate the signal. This digital grating is not a physically manufactured grating, and its structure can be modified to meet different requirements. This offers greater flexibility than classic grating metrology methods, as the shape and size of the digital grating pattern can be flexibly altered digitally. This flexible grating construction allows for a wide range of applications.

[0100] According to some embodiments of the present disclosure, Figure 5 As shown, step S103 is specifically implemented as follows:

[0101] Step S201: After measurement, performing light intensity integration on the first synthetic grating pattern to obtain a first light intensity position relationship curve;

[0102] Step S202: After measurement, performing light intensity integration on the second synthetic grating pattern to obtain a second light intensity position relationship curve;

[0103] Step S203: normalizing the first light intensity position relationship curve and the second light intensity position relationship curve to obtain a normalized differential moiré fringe intensity curve;

[0104] Step S204: obtaining the phase of the differential moiré fringe intensity curve according to a preset phase extraction algorithm, and comparing the phase with a reference phase to obtain a phase change value;

[0105] Step S205: determining the displacement according to a linear relationship between the phase change value and the displacement of the optical grating pattern on the imaging plane.

[0106] Specifically, in order to quantify the displacement value of the projection of the optical grating when it moves on the optical sensor surface, it is necessary to integrate the light intensity of each holding area of ​​the first synthetic grating pattern and the second synthetic grating pattern as follows:

[0107]

[0108]

[0109] Where x, y are the column and row indices in the pixel array, respectively; c is the total number of pixel matrix columns; j is the number of digital grating cycles, which is Figure 4b The digital raster is numbered 1 to 5; I(x, y) is the light intensity value at the pixel coordinate (x, y). 1j and I 2j The first light intensity position relationship curve (which can be referred to as the light intensity curve) I1 and the second light intensity position relationship curve I2 are obtained by connecting them point by point. The intersection of the light intensity curves I1 and I2 is the point where the light intensity is equal (which can be called the alignment point). Figure 6a As shown. Figure 4a When the optical grating image moves up and down in the figure, the I1 and I2 curves will move accordingly, and the alignment point will also move, such as Figure 6a In the figure, when the optical grating moves upward by a distance of ΔP, the alignment point moves from 3 to 4. In practice, uneven illumination intensity may cause variations in I1 and I2. To reduce the influence of light intensity on measurement accuracy, the I1 and I2 curves are normalized to obtain the normalized differential Moire fringe intensity curve I:

[0110]

[0111] Figure 6b For Figure 6aThe corresponding normalized light intensity curve I is: when the alignment point crosses a unit digital grating period, the horizontal displacement of the optical grating image on the optical sensor is ΔP. ​​The alignment points can be counted to obtain the displacement value of the resolution ΔP. The light intensity curve I obtained in the actual measurement is a quasi-sinusoidal curve. The number of sampling points is determined by the size of the digital grating period. The smaller the number of pixel rows occupied by a period, the more sampling points there are. By selecting an appropriate digital grating period, the light intensity curve I for the entire period can be obtained, as shown in the following example: Figure 7 As shown, Figure 7 The number of sampling points in is 40. In order to further improve the accuracy, a phase extraction algorithm can be used to track the phase change of the sine-like curve I. Then the horizontal change ΔD of the optical grating image on the optical sensor is obtained:

[0112]

[0113] Where gratingT is the period of the optical grating.

[0114] Substituting equation (8) into equation (1) yields the phase change It is linearly related to the height change Δh of the measured object:

[0115]

[0116] In actual measurements, because the translation stage's motion is not ideally uniform, the grating moiré fringe signal exhibits nonlinear and non-stationary characteristics. Traditional processing methods such as Fourier decomposition, short-time Fourier decomposition, and wavelet decomposition are not adaptive and cannot obtain accurate phase information.

[0117] Specifically, the preset phase extraction algorithm in step S204 is an adaptive phase extraction algorithm based on the variational mode decomposition (VMD) method. The algorithm first performs variational mode decomposition on the normalized differential moiré fringe intensity curve I obtained above to obtain a series of intrinsic mode functions (IMFs). The fundamental signal is obtained by frequency selection. The fundamental signal obtained at this time still contains a small amount of harmonic components and noise. The fundamental signal after noise reduction is obtained by a second variational mode decomposition. Finally, the phase characteristics of the signal are extracted using the Hilbert transform. Compared with existing methods, the present application has stronger signal decomposition capabilities, anti-noise robustness and non-stationary signal analysis capabilities, and can be effectively applied to phase feature extraction of complex non-stationary signals.

[0118] Therefore, according to some embodiments of the present disclosure, Figure 8 As shown, the above step S204 can be implemented as follows:

[0119] Step S301: performing fast Fourier transform on the differential moiré fringe intensity curve to obtain a corresponding spectrum;

[0120] Based on the collected experimental data, we know that due to factors such as grating processing accuracy and lens size, the actual normalized differential moiré fringe intensity curve I (hereinafter referred to as "intensity curve I") is a quasi-sinusoidal signal between a triangle wave and a sine wave. A signal model for intensity curve I was constructed using the MATLAB platform. It consists of three signals of different frequencies and Gaussian white noise, and its expression is:

[0121] I(x)=sin(2πf1x)+0.1sin(6πf1x)+0.05sin(10πf1x)+n(x) (10)

[0122] Where f1 is the spatial frequency of the optical grating, which is set to 50Hz in this example. The first term represents the fundamental signal of the moiré fringe, and the second and third terms represent the third and fifth harmonic signals of the moiré fringe, respectively. The last term is the noise component present in the process of the optical sensor reading the light intensity signal, and the signal-to-noise ratio is set to 40dB. The time domain waveform of the simulated light intensity curve I signal is as follows: Figure 9 shown.

[0123] The time domain signal I(x) of the light intensity curve is converted into the frequency domain signal I by fast Fourier transform * (ω), frequency domain signal, such as Figure 10 As shown, Figure 10 The Y-axis is amplitude (dB) and the X-axis is frequency (Hz). The simulation signal mainly consists of three frequencies: 50Hz, 150Hz, and 250Hz.

[0124] Step S302: determining the modal decomposition level K value according to the number of harmonics contained in the spectrum;

[0125] Specifically, the K value is equal to the number of frequencies contained in the moiré fringe frequency domain signal plus one. From the previous step, it can be seen that the original signal in this example contains three different frequencies, that is, K is 4.

[0126] Step S303: performing a first variational mode decomposition on the differential moiré fringe intensity curve according to the K value to obtain a series of intrinsic mode functions;

[0127] Specifically, the number of signal decompositions K is equal to 4, and the quadratic penalty coefficient α is set to the default value of 2000. Figure 11 are the time domain signals of each intrinsic mode function (IMF) component obtained after variational mode decomposition.

[0128] Step S304: performing a fast Fourier transform on each of the intrinsic mode functions to obtain a first fundamental wave signal;

[0129] Specifically, Figure 12 is the frequency domain signal of each eigenmode function component. Figure 12 As shown in FIG, the moiré fringe signal is divided into K eigenmode functions according to different frequencies.

[0130] Step S305: performing a second variational mode decomposition on the first fundamental signal to obtain a second fundamental signal after noise reduction;

[0131] Specifically, the intrinsic mode function containing the fundamental wave information is called the fundamental wave IMF signal. The fundamental wave IMF signal is determined according to the theoretically calculated moiré fringe signal. The theoretical frequency is f0 obtained from the spatial frequency of the optical grating. The frequency of the intrinsic mode function IMF-k signal is set to f k (k=1,2,3,4), since the first frequency in the frequency domain of the fundamental IMF signal is usually very close to the theoretical frequency f0, the criterion for judging the fundamental IMF signal can be expressed as f when the following relationship is satisfied k :

[0132] min|f k -f0|

[0133] Depend on Figure 12 It can be seen that the fundamental IMF signal in this example is IMF-1. The second variational mode decomposition is performed on IMF-1. The second decomposition mainly plays the role of a filter. In order to improve the calculation speed of the phase extraction algorithm and reduce the bandwidth of the decomposed IMF signal, the number of signal decompositions K = 2 and the quadratic penalty coefficient α = 10000 are set. The decomposition results are as follows: Figure 13 As shown in , the decomposed center frequencies are sorted from small to large, and the first signal obtained after the second decomposition is the fundamental signal. Figure 14 As shown in the figure, by comparing the frequency domain waveforms of the original signal of the moiré fringe, the first fundamental signal (IMF-1 signal after the first variational mode decomposition), and the second fundamental signal (IMF-1 signal after the second variational mode decomposition), it can be seen that after two variational mode decompositions, the fundamental signal contains only one frequency component.

[0134] Furthermore, in this phase extraction algorithm, the filtering function of the second variational mode decomposition is very necessary. When the noise component in the simulated moiré fringe signal is increased from 40dB to 20dB, the result of the first variational mode decomposition is as follows: Figure 15As shown in the figure, since the amplitude of the noise signal is close to the fifth harmonic signal, the fifth harmonic and noise components cannot be accurately distinguished during the first variational mode decomposition process. There are two frequencies, the fundamental wave and the fifth harmonic, in the IMF-1 signal, and the second variational mode decomposition is required to further strip off the frequencies.

[0135] Step S306: performing Hilbert transform on the second fundamental wave signal to obtain the phase of the differential moiré fringe intensity curve.

[0136] Specifically, according to the definition of Hilbert transform, given a signal x(t), its corresponding Hilbert transform It can be expressed as:

[0137]

[0138] It can be seen that the Hilbert transform of x(t) is x(t) and convolution.

[0139] Perform Fourier transform on the above formula:

[0140]

[0141] From the above formula, we can see that for positive frequencies, the Hilbert transform operation is to delay the phase of all frequency components in the signal by 90°. The analytical signal Z(t) can be constructed:

[0142]

[0143] Among them, x(t) can be expressed as the fundamental signal obtained after the second variational mode decomposition signal, then the instantaneous amplitude of the analytical signal is Instantaneous phase Calculate the phase variable at two moments The two moments can be understood as measuring different positions on the surface of the object being measured.

[0144] Furthermore, the horizontal displacement variation ΔD of the optical grating pattern on the optical sensor can be obtained according to formula (8), that is, the displacement obtained in step S103.

[0145] Step S104: determining the height of the surface of the object to be measured according to the linear relationship between the displacement and the height of the surface of the object to be measured.

[0146] Specifically, the linear relationship between the displacement and the height of the surface of the measured object is expressed as formula (1). According to formula (1) and the displacement obtained in step S103, the height of the surface of the measured object or the height change can be obtained.

[0147] Furthermore, since formula (9) can be obtained according to formula (1) and formula (8), it is also possible to directly use formula (9) and phase variable The height change of the surface topography of the measured object is obtained.

[0148] This application proposes a specific phase extraction algorithm, which can break through the physical limits of sensor pixels and thus improve resolution. In this phase extraction algorithm, by constructing a normalized light intensity difference curve, the sensitivity to light intensity changes caused by the morphology of the surface of the object being measured can be reduced. The phase extraction algorithm based on variational mode decomposition and fast Fourier transform calculates the surface height of the object being measured, which can further improve the robustness and accuracy of the focusing and leveling measurement system, and realize the use of the same grating to simultaneously achieve large-scale coarse measurement of the height of the object being measured and fine measurement with nanometer precision, thereby reducing the complexity of the system structure.

[0149] The present disclosure also provides a focusing and leveling measurement system, which comprises:

[0150] A light source, used to generate the light beam required for measurement;

[0151] an optical grating located downstream of the light source; the optical grating is imaged on the surface of the object to be measured by the light beam to form an optical grating pattern; the optical grating pattern is further reflected onto an imaging plane of the optical sensor;

[0152] The optical sensor is configured to receive the optical grating pattern;

[0153] A data processing module is in communication with the optical sensor and is configured to implement the following steps:

[0154] Encoding the pixels on the optical sensor to maintain or clear the light intensity signal at the pixel, thereby forming a digital grating pattern; the digital grating has the same duty cycle as the optical grating, and there is a preset difference between their periods;

[0155] forming a composite grating pattern by overlapping the optical grating pattern with the digital grating pattern;

[0156] After measurement, performing light intensity integration on the synthetic grating pattern to determine the displacement of the optical grating pattern on the imaging plane;

[0157] The height of the surface of the object to be measured is determined according to a linear relationship between the displacement and the height of the surface of the object to be measured.

[0158] Optionally, the data processing module is specifically used to:

[0159] Overlapping the optical grating pattern with the digital grating pattern to obtain a first synthetic grating pattern;

[0160] The digital grating pattern code is inverted and then overlapped with the optical grating pattern to obtain a second synthetic grating pattern.

[0161] Optionally, the data processing module is specifically used to:

[0162] After measurement, performing light intensity integration on the first synthetic grating pattern to obtain a first light intensity position relationship curve;

[0163] After measurement, performing light intensity integration on the second synthetic grating pattern to obtain a second light intensity position relationship curve;

[0164] Normalizing the first light intensity position relationship curve and the second light intensity position relationship curve to obtain a normalized differential moiré fringe intensity curve;

[0165] Obtaining the phase of the differential moiré fringe intensity curve according to a preset phase extraction algorithm, and comparing the phase with a reference phase to obtain a phase change value;

[0166] The displacement is determined according to a linear relationship between the phase change value and the displacement of the optical grating pattern on the imaging plane.

[0167] Optionally, the data processing module is further configured to:

[0168] Performing a fast Fourier transform on the differential moiré fringe intensity curve to obtain a corresponding frequency spectrum;

[0169] Determining the modal decomposition level K value according to the number of harmonics contained in the spectrum;

[0170] According to the K value, performing a first variational mode decomposition on the differential moiré fringe intensity curve to obtain a series of intrinsic mode functions;

[0171] Performing a fast Fourier transform on each of the intrinsic mode functions to obtain a first fundamental wave signal;

[0172] Performing a second variational mode decomposition on the first fundamental wave signal to obtain a second fundamental wave signal after noise reduction;

[0173] Performing a Hilbert transform on the second fundamental wave signal to obtain the phase of the differential moiré fringe intensity curve.

[0174] Optionally, the number of signal decompositions of the second variational mode decomposition is set to 2.

[0175] The focusing and leveling measurement system provided in the above-mentioned embodiment of the present application and the focusing and leveling measurement method provided in the embodiment of the present application are based on the same inventive concept and have the same beneficial effects as the methods adopted, operated or implemented therein.

[0176] In order to form the same structure, those skilled in the art can also design a method that is not completely the same as the method described above. In addition, although each embodiment is described above respectively, this does not mean that the measures in each embodiment cannot be used in combination advantageously.

[0177] The above describes the embodiments of the present disclosure. However, these embodiments are for illustrative purposes only and are not intended to limit the scope of the present disclosure. The scope of the present disclosure is defined by the appended claims and their equivalents. Without departing from the scope of the present disclosure, those skilled in the art may make various substitutions and modifications, which are intended to fall within the scope of the present disclosure.

Claims

1. A focusing and leveling measurement method, the method comprising: The optical grating is imaged on the surface of the object to be measured by the light beam illumination to form an optical grating pattern, and the optical grating pattern is further reflected onto the imaging plane of the optical sensor, characterized in that: Encoding the pixels on the optical sensor to maintain or clear the light intensity signal at the pixel, thereby forming a digital grating pattern; the digital grating has the same duty cycle as the optical grating, and there is a preset difference between their periods; Overlapping the optical grating pattern with the digital grating pattern to obtain a first synthetic grating pattern; inverting the digital grating pattern code and overlapping it with the optical grating pattern to obtain a second synthetic grating pattern; After measurement, performing light intensity integration on the synthetic grating pattern to determine the displacement of the optical grating pattern on the imaging plane; determining the height of the surface of the object to be measured according to a linear relationship between the displacement and the height of the surface of the object to be measured; The step of performing light intensity integration on the synthetic grating pattern after the measurement to determine the displacement of the optical grating pattern on the imaging plane comprises: After measurement, performing light intensity integration on the first synthetic grating pattern to obtain a first light intensity position relationship curve; After measurement, performing light intensity integration on the second synthetic grating pattern to obtain a second light intensity position relationship curve; Normalizing the first light intensity position relationship curve and the second light intensity position relationship curve to obtain a normalized differential moiré fringe intensity curve; Obtaining the phase of the differential moiré fringe intensity curve according to a preset phase extraction algorithm, and comparing the phase with a reference phase to obtain a phase change value; determining the displacement according to a linear relationship between the phase change value and the displacement of the optical grating pattern on the imaging plane; The step of obtaining the phase of the differential moiré fringe intensity curve according to a preset phase extraction algorithm includes: Performing a fast Fourier transform on the differential moiré fringe intensity curve to obtain a corresponding frequency spectrum; Determining the modal decomposition level K value according to the number of harmonics contained in the spectrum; According to the K value, performing a first variational mode decomposition on the differential moiré fringe intensity curve to obtain a series of intrinsic mode functions; Performing a fast Fourier transform on each of the intrinsic mode functions to obtain a first fundamental wave signal; Performing a second variational mode decomposition on the first fundamental wave signal to obtain a second fundamental wave signal after noise reduction; Performing a Hilbert transform on the second fundamental wave signal to obtain the phase of the differential moiré fringe intensity curve.

2. The focusing and leveling measurement method according to claim 1, characterized in that: The number of signal decompositions of the second variational mode decomposition is set to 2.

3. A focusing and leveling measurement system, characterized in that: include: A light source, used to generate the light beam required for measurement; an optical grating located downstream of the light source; the optical grating is imaged on the surface of the object to be measured by the light beam to form an optical grating pattern; the optical grating pattern is further reflected onto an imaging plane of the optical sensor; The optical sensor is configured to receive the optical grating pattern; A data processing module is communicatively connected to the optical sensor and is used to implement the focusing and leveling measurement method according to claim 1.

4. The focusing and leveling measurement system according to claim 3, characterized in that: The number of signal decompositions of the second variational mode decomposition is set to 2.

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