Overlay response separation and peak positioning method for thickness measurement of ultrathin multilayer transparent material in spectral confocal

Abstract

The invention discloses an overlapping response separation and peak positioning method for thickness measurement of an ultrathin multilayer transparent material in spectral confocal. The method comprises the following steps: 1, acquiring a spectral confocal calibration spectrum and a transparent material overlapping response spectrum; 2, evaluating random noise distribution, and obtaining an intensity detection threshold value and a shape coefficient; 3, obtaining an overlapping response initial peak value position by using the second derivative of the overlapping response spectrum; 4, calculating a generalized Gaussian function fitting initial parameter of overlapping response; 5, iterating the overlapping response parameters until the fitting residual change before and after iteration meets the precision requirement; 6, discarding overlapping responses which do not meet the measurement constraint; 7, the step 5 and the step 6 are executed again until all the overlapping responses meet the measurement constraint, and the peak value position of each overlapping response is obtained. According to the invention, the separation of spectrum confocal overlapping response is realized, the peak value positioning precision is improved, and the thickness of the ultrathin multilayer transparent material can be measured.

Description

Technical Field

[0001] The invention relates to the technical field of transparent material thickness measurement, and in particular to an overlapping response separation and peak positioning method for thickness measurement of ultra-thin multi-layer transparent materials in spectral confocal. Technical Background

[0002] Spectral confocal measurement technology is developed from confocal microscopy measurement technology. It uses the axial dispersion of the dispersive objective to encode the wavelength and position information of the light emitted by the wide spectrum light source. The spectrum detection device then detects the focused light wave reflected from the surface of the object being measured. The peak wavelength is decoded into position information through the spectral confocal signal processing method. This technology has important value in microscopic contour detection and reconstruction due to its high efficiency and high precision, and has been applied to industrial detection, biomedicine and other fields.

[0003] Spectral confocal microscopy can quickly measure the thickness of transparent materials by simultaneously acquiring and processing the spectral responses of different surfaces. However, the responses of different surfaces of ultra-thin transparent materials may overlap, resulting in peak positioning errors and limiting the minimum measurable thickness. Current spectral confocal signal processing algorithms focus on improving the peak wavelength extraction of non-overlapping spectral responses, or dividing partially overlapping wavelength sequences into regions and then obtaining the response peak position in each region. There are limitations in separating and extracting severely overlapping spectral responses. Summary of the invention

[0004] The present invention aims to solve the deficiencies of the above-mentioned prior art and proposes an overlapping response separation and peak positioning method for measuring the thickness of ultra-thin multi-layer transparent materials in spectral confocal, in order to separate severely overlapping spectral responses, expand the lower limit of the thickness of transparent materials that can be measured by spectral confocal, and improve the peak positioning accuracy, so as to measure the thickness of ultra-thin multi-layer transparent materials.

[0005] In order to achieve the above-mentioned purpose, the present invention adopts the following technical scheme:

[0006] The overlapping response separation and peak location method for measuring the thickness of ultra-thin multi-layer transparent materials in spectral confocal imaging of the present invention is characterized in that it includes:

[0007] S1, obtain spectral confocal calibration spectrum Overlapping response spectrum with transparent materials , and the transparent material overlaps the response spectrum Divided into random noise spectrum front band , Spectral confocal working band and the random noise spectrum back band ,in, Represents overlapping response spectra The wavelength starting point, Represents overlapping response spectra The wavelength end point, Indicates the wavelength starting point of the spectral confocal working band, Indicates the wavelength end point of spectral confocal operation and satisfies ;

[0008] S2, based on the random noise spectrum front band and the random noise spectrum back band The spectral mean and standard deviation , evaluate the overlapping response spectra of transparent materials The random noise distribution in ;

[0009] Overlapping response spectra of transparent materials The mean and random noise distribution, the intensity detection threshold is obtained using formula (1) ;

[0010] (1)

[0011] The spectrum is confocally calibrated using a generalized Gaussian function Perform the fitting and take the shape coefficient of the fitting result corresponding to the minimum residual as The shape factor of any overlapping response in ;

[0012] S3, the overlapping response spectrum The internal intensity is above the intensity detection threshold The spectrum of Any The initial peak position of the overlapping response ,in, , represents the number of overlapping responses;

[0013] S4, calculation The initial parameters of the generalized Gaussian function fitting of overlapping responses are: The initial parameters of the overlapping responses are recorded as ,in, , , Respectively The initial peak intensity, initial central wavelength and initial standard deviation of the overlapping responses;

[0014] S5, yes The initial parameters of the overlapping responses are Levenberg-Marquardt iterated until the fitting residual changes before and after the iteration meet the accuracy requirements, thus obtaining The final parameters of overlapping responses, where The final parameters of the overlapping responses are recorded as ,in, , , Respectively Overlapping responses The peak intensity after iterations, The central wavelength after the iteration, The standard deviation after iterations;

[0015] S6, determine whether formula (2) is valid. If so, continue to determine the next peak intensity and center wavelength. Otherwise, discard Then, execute S7;

[0016] (2)

[0017] S7, discard the The final parameters of the remaining overlapping responses are processed until the final parameters of all overlapping responses satisfy equation (2), so that each central wavelength in the final parameters satisfying equation (2) is taken as The peak positions of the corresponding overlapping responses in .

[0018] The overlapping response separation and peak location method for measuring the thickness of ultra-thin multi-layer transparent materials in spectral confocal according to the present invention is also characterized in that S4 comprises:

[0019] First The initial peak position of the overlapping response As the The initial center wavelength of the overlapping response ;

[0020] Using formula (3), we can get The initial standard deviation of the overlapping responses :

[0021] (3)

[0022] In formula (3), express At the center wavelength The full width at half maximum at

[0023] Using formula (4), we can get The initial peak intensity of the overlapping response :

[0024] (4)

[0025] In formula (4), For the The initial center wavelength of the overlapping response, For the The initial standard deviation of the overlapping responses, for exist The strength of for exist The strength of the place.

[0026] Furthermore, the objective function of the Levenberg-Marquardt iteration in S5 is As shown in formula (5):

[0027] (5)

[0028] In formula (5), Indicates Overlapping responses in The generalized Gaussian function fitting results under iterations;

[0029] The update formula of Levenberg-Marquardt iteration in S5 is shown in formula (6):

[0030] (6)

[0031] In formula (6), Indicates Overlapping responses in The generalized Gaussian function fitting results under iterations are: For the The Jacobi matrix of the spectral response at the iteration, is the identity matrix, is the damping coefficient, represents transpose; Indicates The parameters of all response components at iterations, and , Indicates The parameters of all response components at iterations, and ;

[0032] The stopping condition of the Levenberg-Marquardt iteration in S5 is shown in formula (7):

[0033] (7)

[0034] In formula (7), represents the root mean square error, , Respectively represent Generation The fitted residuals of the generation, and , , Indicates the accuracy threshold.

[0035] An electronic device of the present invention includes a memory and a processor, wherein the memory is used to store a program that supports the processor to execute the overlapping response separation and peak location method, and the processor is configured to execute the program stored in the memory.

[0036] The present invention provides a computer-readable storage medium, wherein a computer program is stored on the computer-readable storage medium, and the computer program executes the steps of the overlapping response separation and peak location method when executed by a processor.

[0037] Compared with the prior art, the present invention has the following beneficial effects:

[0038] 1. In step 3, the present invention performs differential differentiation on the overlapping response spectrum to obtain the second-order derivative, and uses the position of the second-order derivative minimum point as the initial peak position of the overlapping response, thereby improving the separation capability of severely overlapping spectral responses and improving the accuracy of the initial peak position;

[0039] 2. The present invention uses a generalized Gaussian function to fit the overlapping response. In step 2, the calibration spectrum is fitted. The obtained shape coefficient can improve the fitting effect of the actual spectral confocal response, and the shape coefficient does not need to be used as an iteration parameter, which ensures that the proposed method can take into account both fitting performance and iteration efficiency. In step 4, the generalized Gaussian function and the spectral confocal response characteristics are combined when calculating the initial parameters of the overlapping response, and high-precision iterative initial parameters can be obtained, thereby greatly reducing the iteration time.

[0040] 3. The present invention judges the overlapping response parameters after iteration in step 6, discards the false response by measuring the constraint, and re-iterates the remaining overlapping response parameters, thereby avoiding the misdetection of the false overlapping response. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 A flow chart of the overlapping response separation and peak location method of the present invention;

[0042] Figure 2It is a schematic diagram of the overlapping response spectrum of transparent materials and the initial value estimation of the overlapping response position of the overlapping response separation and peak location method of the present invention;

[0043] Figure 3 This is a diagram of overlapping response initial value estimation and iterative optimization results of the overlapping response separation and peak location method of the present invention. DETAILED DESCRIPTION

[0044] In this embodiment, a method for separating overlapping responses and locating peak values ​​for measuring the thickness of ultra-thin multilayer transparent materials in spectral confocal imaging is provided. Figure 1 As shown, the following steps are included:

[0045] S1, obtain spectral confocal calibration spectrum Overlapping response spectrum with transparent materials , and overlap the response spectrum of transparent materials Divided into random noise spectrum front band , Spectral confocal working band and the random noise spectrum back band ,in, Represents overlapping response spectra The wavelength starting point, Indicates the wavelength starting point of the spectral confocal working band, Indicates the wavelength end point of spectral confocal operation, Represents overlapping response spectra The wavelength end point;

[0046] like Figure 2 As shown, the spectral confocal working band contains both overlapping responses and random noise, and and contains only random noise spectra, so it is used to evaluate the random noise distribution.

[0047] S2, spectral confocal random noise mainly comes from the dark noise of the light source and detector, which can be regarded as Gaussian white noise. and the random noise spectrum back band The spectral mean and standard deviation , evaluate the overlapping response spectra of transparent materials The random noise distribution in ;

[0048] Overlapping response spectra based on transparent materials The mean and random noise distribution, the intensity detection threshold is obtained using formula (1) ;

[0049] (1)

[0050] Using Generalized Gaussian Function to Calibrate Spectra Confocally Perform the fitting and take the shape coefficient of the fitting result corresponding to the minimum residual as The shape factor of any overlapping response in ;

[0051] Form Factor The value of is affected by the spectral power distribution of the light source, the numerical aperture of the dispersion objective lens, and the surface characteristics of the sample being measured. Therefore, under the same measurement settings, the confocal calibration spectrum is fitted. The resulting shape factor It is also suitable for fitting overlapping response spectra of transparent materials , shape factor Once the value is determined, it does not need to be changed.

[0052] S3, response spectra for overlap The internal intensity is higher than the intensity detection threshold The spectrum of Any The initial peak position of the overlapping response ,in, , represents the number of overlapping responses;

[0053] Preferably, Gaussian smoothing is performed on the obtained second-order derivative to reduce interference of random noise on acquisition of initial peak position of overlapping response;

[0054] Initial peak position of overlapping response The acquisition of Figure 2 The enlarged part on the right shows the minimum position of the second-order derivative and the initial peak position of the overlapping spectral response. Corresponding.

[0055] S4, calculation The initial parameters of the generalized Gaussian function fitting of overlapping responses are: The initial parameters of the overlapping responses are recorded as ,in, , , Respectively The initial peak intensity, initial central wavelength and initial standard deviation of the overlapping responses;

[0056] Specifically, using formula (2) we get The initial generalized Gaussian function fitting results of overlapping responses :

[0057] (2)

[0058] First The initial peak position of the overlapping response As the The initial center wavelength of the overlapping response ;

[0059] Using formula (3), we can get The initial standard deviation of the overlapping responses :

[0060] (3)

[0061] In formula (3), express At the center wavelength The full width at half maximum at

[0062] Due to the mutual influence between overlapping responses, directly adopting The value at the center wavelength is inaccurate as the initial peak intensity. Therefore, using formula (4) to obtain The initial peak intensity of the overlapping response :

[0063] (4)

[0064] In formula (4), For the The initial center wavelength of the overlapping response, For the The initial standard deviation of the overlapping responses, for exist The strength of for exist The strength of the place;

[0065] And, we can use formula (5) to get The adjacent The initial peak intensity of the overlapping response :

[0066] (5)

[0067] like Figure 3 As shown in (a), the initial overlapping response superposition Overlapping spectral response with transparent materials The fit is good, but the initial overlapping responses There are false overlapping responses caused by random noise.

[0068] S5, yes The initial parameters of the overlapping responses are Levenberg-Marquardt iterated until the fitting residual changes before and after the iteration meet the accuracy requirements, thus obtaining The final parameters of overlapping responses, where The final parameters of the overlapping responses are recorded as ,in, , , Respectively Overlapping responses The peak intensity after iterations, The central wavelength after the iteration, The standard deviation after iterations;

[0069] Objective function of the Levenberg-Marquardt iteration As shown in formula (6):

[0070] (6)

[0071] In formula (6), Indicates Overlapping responses in The generalized Gaussian function fitting results under iterations;

[0072] The update formula of Levenberg-Marquardt iteration is shown in formula (7):

[0073] (7)

[0074] In formula (7), Indicates Overlapping responses in The generalized Gaussian function fitting results under iterations are: For the The Jacobi matrix of the spectral response at the iteration, is the identity matrix, is the damping coefficient, represents transpose; Indicates The parameters of all response components at iterations, and , Indicates The parameters of all response components at iterations, and ;

[0075] The stopping condition of Levenberg-Marquardt iteration is shown in formula (8):

[0076] (8)

[0077] In formula (8), represents the root mean square error, , Respectively represent Generation The fitted residuals of the generation, and , , represents the accuracy threshold; preferably, the accuracy threshold Take 0.001.

[0078] S6, determine whether formula (9) is valid. If so, continue to determine the next peak intensity and center wavelength. Otherwise, discard Then, execute S7.

[0079] (9)

[0080] S7, discard the The final parameters of the remaining overlapping responses are processed until the final parameters of all overlapping responses satisfy equation (9), so that each central wavelength in the final parameters satisfying equation (9) is taken as The peak position of the corresponding overlapping response in ;

[0081] like Figure 3 As shown in (b), the false responses that do not meet the measurement constraints have been discarded, and the final overlapping responses are superimposed. Overlapping spectral response with transparent materials The fitting effect is good, and the overlapping response separation and peak positioning of the thickness measurement of ultra-thin multi-layer transparent materials are achieved.

[0082] In this embodiment, an electronic device includes a memory and a processor, wherein the memory is used to store a program that supports the processor to execute the above method, and the processor is configured to execute the program stored in the memory.

[0083] In this embodiment, a computer-readable storage medium stores a computer program on the computer-readable storage medium, and the computer program executes the steps of the above method when executed by a processor.

Claims

1. A method for separating overlapping responses and locating peak values ​​for thickness measurement of ultra-thin multilayer transparent materials in spectral confocal imaging, characterized in that: include: S1, obtain spectral confocal calibration spectrum Overlapping response spectrum with transparent materials , and the transparent material overlaps the response spectrum Divided into random noise spectrum front band , Spectral confocal working band and the random noise spectrum back band ,in, Represents overlapping response spectra The wavelength starting point, Represents overlapping response spectra The wavelength end point, Indicates the wavelength starting point of the spectral confocal working band, Indicates the wavelength end point of spectral confocal operation and satisfies ; S2, based on the random noise spectrum front band and the random noise spectrum back band The spectral mean and standard deviation , evaluate the overlapping response spectra of transparent materials The random noise distribution in ; Overlapping response spectra of transparent materials The mean and random noise distribution, the intensity detection threshold is obtained using formula (1) ; (1) The spectrum is confocally calibrated using a generalized Gaussian function Perform the fitting and take the shape coefficient of the fitting result corresponding to the minimum residual as The shape factor of any overlapping response in ; S3, the overlapping response spectrum The internal intensity is higher than the intensity detection threshold The spectrum of Any The initial peak position of the overlapping response ,in, , represents the number of overlapping responses; S4, calculation The initial parameters of the generalized Gaussian function fitting of overlapping responses are: The initial parameters of the overlapping responses are recorded as ,in, , , Respectively The initial peak intensity, initial central wavelength and initial standard deviation of the overlapping responses; S5, yes The initial parameters of the overlapping responses are Levenberg-Marquardt iterated until the fitting residual changes before and after the iteration meet the accuracy requirements, thus obtaining The final parameters of overlapping responses, where The final parameters of the overlapping responses are recorded as ,in, , , Respectively Overlapping responses The peak intensity after iterations, The central wavelength after the iteration, The standard deviation after iterations; S6, determine whether formula (2) is valid. If so, continue to determine the next peak intensity and center wavelength. Otherwise, discard Then, execute S7; (2) S7, discard the The final parameters of the remaining overlapping responses are processed until the final parameters of all overlapping responses satisfy equation (2), so that each central wavelength in the final parameters satisfying equation (2) is taken as The peak positions of the corresponding overlapping responses in .

2. The overlapping response separation and peak location method for measuring the thickness of ultra-thin multi-layer transparent materials in spectral confocal according to claim 1, characterized in that S4 include: First The initial peak position of the overlapping response As the The initial center wavelength of the overlapping response ; Using formula (3), we can get The initial standard deviation of the overlapping responses : (3) In formula (3), express At the center wavelength The full width at half maximum at Using formula (4), we can get The initial peak intensity of the overlapping response : (4) In formula (4), For the The initial center wavelength of the overlapping response, For the The initial standard deviation of the overlapping responses, for exist The strength of for exist The strength of the place.

3. The overlapping response separation and peak location method for thickness measurement of ultra-thin multi-layer transparent materials in spectral confocal according to claim 2, characterized in that: Objective function of Levenberg-Marquardt iteration in S5 As shown in formula (5): (5) In formula (5), Indicates Overlapping responses in The generalized Gaussian function fitting results under iterations; The update formula of Levenberg-Marquardt iteration in S5 is shown in formula (6): (6) In formula (6), Indicates Overlapping responses in The generalized Gaussian function fitting results under iterations are: For the The Jacobi matrix of the spectral response at the iteration, is the identity matrix, is the damping coefficient, represents transpose; Indicates The parameters of all response components at iterations, and , Indicates The parameters of all response components at iterations, and ; The stopping condition of the Levenberg-Marquardt iteration in S5 is shown in formula (7): (7) In formula (7), represents the root mean square error, , Respectively represent Generation The fitted residuals of the generation, and , , Indicates the accuracy threshold.

4. An electronic device, comprising a memory and a processor, characterized in that: The memory is used to store a program that supports the processor to execute the overlapping response separation and peak location method according to any one of claims 1 to 3, and the processor is configured to execute the program stored in the memory.

5. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the overlapping response separation and peak location method according to any one of claims 1 to 3 are executed.

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