CN117109450B - High-resolution spectrum confocal interference film thickness measuring method for self-adaptive parameter spectrum estimation - Google Patents
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Abstract
The invention discloses a high-resolution spectrum confocal interference film thickness measuring method for self-adaptive parameter spectrum estimation, which comprises the steps that firstly, light generated by a broadband light source LS passes through an optical fiber coupler, is respectively coupled to a reference arm and a sample arm S through two ports on the left side according to a preset proportion, is scattered by a sample surface and a reference surface, returns to the optical fiber coupler to generate interference, and finally is irradiated to a diffraction grating G through a convex lens L3 by a light guide optical fiber; the diffraction grating G diffracts interference signals to different positions of a CCD camera lens after passing through the convex lens L4 at different angles according to different wavelengths, and finally the interference signals are captured by a photosensitive element of the CCD camera, and then thickness measurement is carried out by a computer. The method can effectively solve the problem of limited measurement resolution caused by spectrum gaps in the current method.
Description
Technical Field
The invention relates to the field of precise measurement, in particular to a high-resolution spectrum confocal interference film thickness measuring method for self-adaptive parameter spectrum estimation.
Background
The continuous development of precision manufacturing industry has higher and higher requirements on precision measurement technology, such as the thickness of optical films plated on various optical elements, the thickness of different functional film layers in the manufacturing process of liquid crystal displays, and the like, and the requirements on measurement precision cannot be met by adopting traditional high-precision measurement tools such as vernier calipers, micrometer and the like. Therefore, the method realizes high-precision measurement of the thickness of the optical material and has important significance for production and application of the optical material.
The spectral confocal displacement sensor is a novel non-contact photoelectric displacement sensor with high precision and high stability, the method is proposed by the French STIL company in 1995, and is still an accurate and reliable non-contact distance and thickness measuring method recognized in the global scope so far, and the method obtains the geometric thickness of a material, namely the actual thickness by obtaining the corresponding relation between the peak wavelength and the thickness of the material; spectral domain optical coherence tomography is a new generation OCT method proposed by Fercher in 1995, and the method obtains the optical thickness of a material according to amplitude information of signals by extracting amplitude-frequency characteristics of interference signals after Fourier transformation of the spectral signals and then combining the refractive index of the material to obtain the geometric thickness.
The above methods of spectral confocal and spectral domain optical coherence tomography have the defect that simultaneous measurement of material thickness and refractive index cannot be realized. In 2017 Boettcher et al proposed a method of combining spectral confocal with spectral domain optical coherence tomography, namely chromatic confocal coherence tomography (Chromatic Confocal Coherence Tomography, CCCT), by means of a fiber-optic measurement system, simultaneous measurement of thickness and refractive index was achieved without knowledge of the refractive index of the material. One of the problems is: as shown in fig. 1, in the fourier transform process of the interference signal, due to the introduction of the confocal lens, the signal-to-noise ratio of the non-confocal area of the interference signal is extremely low, and the fourier transform is performed on the interference spectrum, so that the side lobe effect caused by the existence of the spectrum gap is extremely serious, and therefore, the actual measurement resolution is not high.
Disclosure of Invention
The invention aims to provide a high-resolution spectrum confocal interference film thickness measuring method for self-adaptive parameter spectrum estimation, which is used for solving the problem of limited measurement resolution caused by spectrum gaps in the current method.
In order to realize the tasks, the invention adopts the following technical scheme:
A high resolution spectral confocal interference film thickness measurement system for adaptive parameter spectrum estimation, comprising:
The device comprises a color confocal probe, a spectrum confocal displacement sensor, a broadband light source, an optical fiber coupler, a diffraction grating and a CCD camera; a sample surface is arranged below the color confocal probe and is used for placing an optical material to be measured; a reference surface corresponding to the sample surface is arranged below the spectral confocal displacement sensor; taking the light path from the chromatic confocal probe to the sample stage as a sample arm S, and taking the light path from the spectral confocal displacement sensor to the reference surface as a reference arm R;
The spectral confocal displacement sensor comprises convex lenses L1 and L2, and convex lenses L3 and L4 are respectively arranged on two sides of the diffraction grating; the L1 and the L3 are used for collimating light rays, and the parallel incident light rays are focused after the L2 and the L4 are aligned;
The left side and the right side of the optical fiber coupler are respectively provided with two ports, the two ports on the left side are respectively connected with the color confocal probe and the spectrum confocal displacement sensor, and the two ports on the right side are respectively connected with the broadband light source LS and the light guide optical fiber.
Further, the working process of the system is as follows:
Firstly, light generated by a broadband light source LS is coupled to a reference arm and a sample arm S respectively through two ports on the left side according to a preset proportion after passing through an optical fiber coupler, and is scattered by a sample surface and the reference surface and then returns to the optical fiber coupler to generate interference, and finally is irradiated to a diffraction grating G through a convex lens L3 by a light guide optical fiber; the diffraction grating G diffracts interference signals to different positions of a CCD camera lens after passing through the convex lens L4 at different angles according to different wavelengths, and finally the interference signals are captured by a photosensitive element of the CCD camera, and then thickness measurement is carried out by a computer.
Further, the light passes through the optical material to be measured having a refractive index n 2, and the optical thickness d int thereof can be expressed as:
dint＝d×n2 (1)
wherein d int is the optical thickness of the optical material, its geometric thickness of the d optical material, the refractive index of the n 2 optical material.
A high resolution spectral confocal interference film thickness measurement method for adaptive parameter spectrum estimation, comprising:
Step 1, carrying out low-pass filtering on interference signals acquired by a measuring light path system aiming at an optical material to be measured, and obtaining confocal thickness d conf through the distance between adjacent peaks of the filtered signals;
Step 2, obtaining the optical thickness d int of the optical material to be measured with high precision by a self-adaptive parameter spectrum estimation method;
Step 3, according to the confocal thickness d conf and the optical thickness d int, and combining the numerical aperture NA of the chromatic confocal probe, the geometric thickness d of the material can be obtained according to the following formula by combining the results, and then the refractive index n 2 can be obtained according to the formula (1):
further, the adaptive parameter spectrum estimation method comprises the following steps:
step 1, obtaining a parameter vector from formula (10) As an initial iteration value, the subscript l represents the first frequency point, and the superscript 0 represents the 0 th iteration;
The superscript T in the above formula represents matrix transposition, A l is a coefficient matrix at a frequency point f l, and I (n) represents an interference signal;
Step 2, obtaining a covariance matrix Γ κ by a formula (12), wherein the upper mark kappa represents the kappa-th iteration;
Wherein Q l is the covariance matrix corresponding to f l, For the amplitude frequency of the spectral peak frequency, A p is a coefficient matrix of the spectral peak frequency, p represents the p-th frequency point of the spectral peak, and L is the total number of frequency points in the interference amplitude frequency;
Step 3, obtaining the optimal parameter vector from the formula (14) The subscript κ represents the kth iteration;
Step 4, judging whether the preset iteration times are reached, if so, carrying out the next Step, otherwise, starting execution from Step 2;
step 5, estimating the optimal parameter vector as the iteration is completed Then the interference amplitude frequency/>, can be obtainedThe method comprises the following steps:
Wherein, The optimal parameter vector is the kappa-th iteration; the values X (f l) of the parameter vector at f l, l=1, 2,..The maximum likelihood estimation of vector X (f l) will be produced during the above-described Step 1 to Step 5 iterations, and as the iterations proceed, vector X (f l) and covariance matrix Γ will also converge gradually;
The interference frequencies f pk1 and f pk2 corresponding to the two spectral peaks are found in the interference amplitude frequency, the positions d pk1 and d pk2 corresponding to the spectral peaks are found, and the absolute value is taken, so that the optical thickness d int can be obtained:
dint＝|dpk1-dpk2| (16)
compared with the prior art, the invention has the following technical characteristics:
The invention adopts a mode of combining spectral confocal and optical coherence tomography of optical fiber type spectral domain to measure the thickness and refractive index of the material. Due to the fact that the confocal lens is introduced, the signal-to-noise ratio of the non-confocal area of the interference signal is extremely low, the side lobe effect at the peak frequency is serious, the peak frequency is difficult to read accurately by the measurement result, the resolution of the measurement result is reduced, the side lobe effect caused by a spectrum gap can be effectively restrained by the self-adaptive parameter spectrum estimation method, and the frequency where the peak is can be accurately extracted. In a specific embodiment, comparing the result after fourier transform with the result of adaptive parameter spectrum estimation, it can be seen from fig. 5 and 6 that the effect of the method is better than fourier transform, the side lobe effect caused by the spectrum gap is effectively suppressed, and high resolution calculation under the spectrum gap can be realized.
Drawings
FIG. 1 is a schematic diagram of a problem in the prior art;
FIG. 2 is a schematic diagram of a measurement light path system for implementing the present application;
FIG. 3 is a schematic diagram of an original signal collected by a CCD camera according to an embodiment of the present invention;
FIG. 4 is a schematic diagram of a confocal signal according to an embodiment of the invention;
FIG. 5 is a schematic diagram of the result of Fourier transform in an embodiment of the invention;
fig. 6 is a schematic diagram of an adaptive parameter spectrum estimation result according to an embodiment of the present invention.
Detailed Description
The invention provides a high-resolution spectral confocal interference film thickness measuring method of self-adaptive parameter spectrum estimation, referring to fig. 2, a measuring Light path system for realizing the thickness measuring method of the invention comprises a chromatic confocal probe (CCP, chromatic Confocal Probe), a spectral confocal displacement sensor, a broadband Light Source (LS), an optical Fiber Coupler (FC), a diffraction Grating (G, graining) and a CCD camera; a sample surface is arranged below the color confocal probe and is used for placing an optical material to be measured; a reference surface corresponding to the sample surface is arranged below the spectral confocal displacement sensor; taking the light path from the color confocal probe to the sample stage as a sample arm (S, SAMPLE ARM), and taking the light path from the spectral confocal displacement sensor to the reference surface as a reference arm (R, REFERENCE ARM); the spectral confocal displacement sensor comprises convex lenses L1 and L2, and convex lenses L3 and L4 are respectively arranged on two sides of the diffraction grating; the L1 and the L3 are used for collimating light rays, and the parallel incident light rays are focused after the L2 and the L4 are aligned;
The left side and the right side of the optical fiber coupler are respectively provided with two ports, the two ports on the left side are respectively connected with the color confocal probe and the spectrum confocal displacement sensor, and the two ports on the right side are respectively connected with the broadband light source LS and the light guide optical fiber;
firstly, light generated by a broadband light source LS is coupled to a reference arm and a sample arm (S, SAMPLE ARM) through two ports on the left side in a ratio of 50:50 after passing through an optical Fiber Coupler (FC), scattered by a sample surface and a reference surface and returned to the optical Fiber Coupler to generate interference, and finally, the interference is irradiated to a diffraction grating G through a convex lens L3 by a light guide optical Fiber; the diffraction grating G diffracts interference signals to different positions of a CCD camera lens after passing through the convex lens L4 at different angles according to different wavelengths, and finally the interference signals are captured by a photosensitive element of the CCD camera, and then thickness measurement is carried out by a computer.
The light passes through the optical material to be measured having a refractive index n 2, and its optical thickness d int can be expressed as:
dint＝d×n2 (1)
wherein d int is the optical thickness of the optical material, its geometric thickness of the d optical material, the refractive index of the n 2 optical material.
Based on the system, the specific implementation steps of the high-resolution spectrum confocal interference film thickness measurement method for self-adaptive parameter spectrum estimation are described.
Step 1, low-pass filtering is performed on interference signals obtained by using a measuring light path system for an optical material to be measured, and the confocal thickness d conf is obtained through the distance (corresponding confocal depth) between adjacent peaks of the filtered signals.
Step 2, obtaining the optical thickness d int of the optical material to be measured with high precision by a self-adaptive parameter spectrum estimation method; the adaptive parameter spectrum estimation method specifically comprises the following steps:
The inner part of the optical material to be measured is M discrete interface layers, when the direct current component and the autocorrelation component are ignored, the interference signal collected by the CCD camera can be expressed as superposition of a plurality of sine signals, and the frequency of the sine signals represents different interface layers in the optical material to be measured, so that the interference signal I (k) can be rewritten as:
wherein, the subscript M represents the M-th interface layer, M discrete interface layers are altogether, alpha R and alpha m respectively represent the reflection light intensities of the reference surface and the M-th interface layer inside the optical material to be measured, and z R and z Lm respectively represent the optical paths of the reference surface and the M-th interface layer inside the optical material to be measured; k=2pi/λ represents the output wave number of the laser light of the broadband light source, and λ is the laser wavelength;
When synthesizing wavenumbers, the discrete form k (n) of wavenumber k can be described as:
In the above formula, J represents the J-th wavelength band, the center wavelength and bandwidth of the wavelength band are represented as lambda Cj and delta lambda j respectively, and J scanning wavelength bands are provided; n is the number of sampling points in each wavelength band, n=1, 2, …, j·n is the nth sampling point in the sampling point sequence, and j·n total sampling points. Epsilon (x) is a step function, and when x.gtoreq.0, the value of x < 0 is 1 and the value of x < 0 is 0. In the formula 3, x represents N- (j-1). N-1.
Substituting equation (3) into equation (2) and linearizing in the wavenumber domain by interpolation, the interference signal I (n) under wavenumber synthesis can be expressed as:
Where λ Cj denotes a center wavelength of the jth wavelength scan segment, Δλ j denotes a bandwidth of the jth wavelength scan segment, and Λ Rm denotes an optical path difference between the reference plane and the mth interface layer.
Equation (5) is to reconstruct depth information of the optical material to be measured from the interference signal shown in equation (4), and the spectrum of the interference signal needs to be estimated, and the current standard demodulation algorithm uses discrete fourier transform to estimate:
Where i represents an imaginary unit, f represents a frequency point, Is the spectrum of the interference signal, i.e. the fourier transform of the interference signal at the frequency point f.
As can be seen from the formula (4), the initial phase of the interference signal is 4pi Λ Rm/(λCj-Δλj/2, and as different wavenumber segments in the broadband light source output wavenumber have different center wavelengths and bandwidths, the initial phase is necessarily changed, so that the light intensity distribution is discontinuous, at the moment, samples of the interference signal continuously collected by the CCD camera are lost, and the interference amplitude frequency obtained by demodulating the interference signal by using the formula (5) is also distorted in frequency spectrum due to side lobe abnormality.
The interference spectrum is theoretically a discrete spectrum, has the characteristic of sparseness in a frequency domain, can be modified by adopting a least square method to the formula (5), and constructs the following optimization model in a wave number domain:
in the formula (6), only the true interference spectrum is estimated When the optimization model can realize minimization, the optimization of the formula (6) has the opportunity to solve the problem that the interference spectrum has side lobe abnormality when the mode jump exists in the broadband light source output wave number.
As can be seen from the formula (5),For complex value, there is amplitude-frequency information and phase-frequency information, so that/>The rewriting is as follows:
where || denotes the value after fourier transformation of the interference signal, i.e. amplitude-frequency information, I.e./>Amplitude-frequency information of (a), i.e. amplitude at frequency point f, phi (f) is/>Phase angle at frequency point f. Substituting equation (7) into equation (6), and by the euler equation, the least squares optimization model can be rewritten as:
The interference signal expression represented by equation (4) knows I (n) ∈r, where the first term in equation (8) is of fitting significance, while the second term is not interpreted by a data fit, so the latter acts as an additive disturbance on the first term only, independent of the data. When the estimated interference spectrum has amplitude and phase in other frequency regions than the interference frequency, new sinusoidal components must be introduced into the error equation, which leads to an increase in error. Therefore, the least square optimization model is optimized, the obtained interference spectrum is closer to the real spectrum, and meanwhile, window function convolution operation in a transform domain algorithm is avoided, and the problem that the spectrum is distorted due to the influence of window function convolution is solved.
To solve the above optimization problem, when only a certain specific frequency point f l (i represents the frequency of the first frequency point, and is any one of values [1, L ], where L is the total number of frequency points) is considered, and the second term that is the additive disturbance is ignored, equation (8) can be expanded into an interference spectrum sparse optimization matrix model:
Wherein, "||" denotes euclidean norms, a l is a coefficient matrix at a specific frequency point f l, For fourier transformation at a specific frequency point f l, and X l is a parameter vector to be solved containing interference amplitude and phase frequency information, the parameter vector X l at each frequency point f l can be obtained by a matrix least squares algorithm:
The superscript T in the above equation denotes the matrix transpose.
In the optimization model represented by equation (9), in addition to the sinusoidal component with frequency f l that may exist, other sinusoidal components with different frequencies and noise may be included in I (n). For ease of analysis, the noise component in the interference signal is not explicitly considered here, but rather as an observation error for each sample point. Definition matrix Q l is shown in equation (11), which can be considered as the covariance matrix of the sinusoidal components in I (n) that may exist in addition to frequency f l:
Wherein f p is the frequency corresponding to the maximum amplitude in the interference amplitude frequency, p represents that the frequency point of the spectral peak is the p-th frequency point, L is the L-th frequency point in the frequency, L is the total number of frequency points in the interference amplitude frequency, For the amplitude frequency at the spectral peak frequency, a p is the coefficient matrix at the spectral peak frequency. The covariance matrix Q l gives different weights to each frequency point, and when the position of the frequency f p is a spectrum peak, the formula (11) can know that the frequency f p has a larger weight, which is positive for the contribution of the spectrum peak identification of the interference spectrum, so that the weighted least square method has higher calculation accuracy. It is worth noting, however, that in calculating the interference spectrum, for each point on the frequency f l, l=1, 2, …, it is necessary to calculate the covariance matrix Q l corresponding to f l, which would have a very large computational complexity in the case of N > > 1. Thus, a matrix Γ can be introduced as shown in equation (12), which is consistent for any frequency point f l, so that the matrix Γ can be calculated only once and applied to the weighted least squares calculation of any frequency point f l, thereby reducing the computational complexity:
When matrix Γ is present and reversible, formula (9) is modified using a weighted least squares method:
[ I-A lXl]TΓ-1[I-AlXl ] (13) the parameter vector X l can be calculated by a matrix weighted least squares algorithm:
In the above process, the matrix Γ is a matrix superposition on all frequency points. However, the weight distribution of each frequency point is not clear, and the matrix Γ and the optimal estimation calculated by the weight distribution are not accurate. Aiming at the problem, the adaptive parameter spectrum estimation algorithm adopts an iterative mode to gradually increase the weight of the frequency point at the position of the spectrum peak, and gradually reduces the weight of the frequency point of the non-spectrum peak, and the steps of the algorithm can be summarized as follows:
step 1, obtaining a parameter vector from formula (10) As an initial iteration value, the subscript l represents the first frequency point, and the superscript 0 represents the 0 th iteration;
Step 2, obtaining a covariance matrix Γ κ by a formula (12), wherein the upper mark kappa represents the kappa-th iteration;
Step 3, obtaining the optimal parameter vector from the formula (14) The subscript κ represents the kth iteration;
Step 4, judging whether the preset iteration times are reached, if so, carrying out the next Step, otherwise, starting execution from Step 2;
step 5, estimating the optimal parameter vector as the iteration is completed Then the interference amplitude frequency/>, can be obtainedThe method comprises the following steps:
Wherein, Is the optimal parameter vector for the kth iteration. The values X (f l) of the parameter vector at f l, l=1, 2,..The adaptive parameter spectrum estimation algorithm will produce a maximum likelihood estimate of vector X (f l) during the above-described Step 1 to Step 5 iteration, and as the iteration proceeds, vector X (f l) and covariance matrix Γ will also converge gradually. Through the calculation, the obtained interference amplitude frequency energy is concentrated, and side lobes can be effectively suppressed, so that the positions of adjacent spectrum peaks can be more easily distinguished, the interference frequency f pk of the positions can be obtained, and compared with fig. 5, the side lobes are effectively suppressed, and the interference frequency of the positions can be more easily obtained.
Because the optical material to be measured has a certain thickness and has upper and lower surfaces, two spectral peaks exist in interference amplitude frequency, interference frequencies f pk1 and f pk2 corresponding to the two spectral peaks can be found in the interference amplitude frequency by calculating amplitude frequency information of the interference spectrum, positions d pk1 and d pk2 corresponding to the spectral peaks are found, and the absolute value is taken, so that the optical thickness d int can be obtained.
dint＝|dpk1-dpk2| (16)
Step 3, combining the confocal thickness d conf obtained in step 1 and the optical thickness d int obtained in step 2 with the numerical aperture NA (fixed value determined by lens design) of the chromatic confocal probe, and combining the results, the geometric thickness d of the material can be obtained according to formula (17), and then the refractive index n 2 can be obtained according to formula (1). The method combines the confocal thickness d conf and the optical thickness d int, and can calculate the geometric thickness d and the refractive index n 2 of the material respectively.
Examples:
1) According to the construction of the optical path structure shown in fig. 2, the optical material to be measured is placed on the sample surface under the chromatic confocal probe, and is fixed by using the clamping piece fixture.
2) FIG. 3 is an original signal acquired using an interference signal acquired by a CCD camera;
3) The original signal shown in fig. 3 is subjected to low-pass filtering, so that a confocal result shown in fig. 4 can be obtained, and the confocal thickness d conf can be 0.9mm according to the distance between the signal peaks.
4) After high-pass filtering is performed on the original signal shown in fig. 3, fourier transformation is directly performed according to the original method, and the result shown in fig. 5 can be obtained. As can be seen from the results shown in fig. 5, since the original signal is affected by confocal imaging, there is a gap in the interference spectrum, so that the side lobe effect at the peak frequency is serious, the measurement result is difficult to accurately read the peak value, and the measurement resolution is low.
5) After the self-adaptive parameter spectrum estimation provided by the invention is used for replacing the traditional Fourier transform, a spectrum result shown in figure 6 can be obtained, and the result can be used for effectively inhibiting side lobe effect caused by spectrum gaps and accurately extracting the frequency of a peak value.
From the distance between the signal peaks in fig. 6, d int =2.02 mm can be obtained, and in combination with the confocal thickness d conf =0.9 mm, the numerical aperture of the chromatic confocal probe used in this embodiment is na=sin13°, and as calculated by substituting formula (17), the geometric thickness of the optical material is 1.3581mm, and the refractive index is 1.4874.
The above embodiments are only for illustrating the technical solution of the present application, and are not limiting; although the application has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical scheme described in the foregoing embodiments can be modified or some technical features thereof can be replaced by equivalents; such modifications and substitutions do not depart from the spirit and scope of the technical solutions of the embodiments of the present application, and are intended to be included in the scope of the present application.
Claims (1)
1. The utility model provides a high resolution spectrum confocal interference film thickness measurement system of self-adaptation parameter spectrum estimation which characterized in that includes:
The device comprises a color confocal probe, a spectrum confocal displacement sensor, a broadband light source, an optical fiber coupler, a diffraction grating and a CCD camera; a sample surface is arranged below the color confocal probe and is used for placing an optical material to be measured; a reference surface corresponding to the sample surface is arranged below the spectral confocal displacement sensor; taking a light path from the color confocal probe to the sample stage as a sample arm S, and taking a light path from the spectral confocal displacement sensor to a reference surface as a reference arm R;
The spectral confocal displacement sensor comprises convex lenses L1 and L2, and convex lenses L3 and L4 are respectively arranged on two sides of the diffraction grating; the L1 and the L3 are used for collimating light rays, and the parallel incident light rays are focused after the L2 and the L4 are aligned;
The left side and the right side of the optical fiber coupler are respectively provided with two ports, the two ports on the left side are respectively connected with the color confocal probe and the spectrum confocal displacement sensor, and the two ports on the right side are respectively connected with the broadband light source LS and the light guide optical fiber;
The working process of the system is as follows:
Firstly, light generated by a broadband light source LS is coupled to a reference arm and a sample arm S respectively through two ports on the left side according to a preset proportion after passing through an optical fiber coupler, and is scattered by a sample surface and the reference surface and then returns to the optical fiber coupler to generate interference, and finally is irradiated to a diffraction grating G through a convex lens L3 by a light guide optical fiber; the diffraction grating G diffracts interference signals to different positions of a CCD camera lens after passing through the convex lens L4 at different angles according to different wavelengths, and finally the interference signals are captured by a photosensitive element of the CCD camera, and then thickness measurement is carried out by a computer;
the light passes through the optical material to be measured having a refractive index n 2, and its optical thickness d int is expressed as:
dint＝d×n2 (1)
wherein d int is the optical thickness of the optical material, its geometric thickness of the d optical material, the refractive index of the n 2 optical material;
The high-resolution spectrum confocal interference film thickness measurement method based on the self-adaptive parameter spectrum estimation of the thickness measurement system comprises the following steps:
Step 1, carrying out low-pass filtering on interference signals acquired by a measuring light path system aiming at an optical material to be measured, and obtaining confocal thickness d conf through the distance between adjacent peaks of the filtered signals;
Step 2, obtaining the optical thickness d int of the optical material to be measured with high precision by a self-adaptive parameter spectrum estimation method;
The adaptive parameter spectrum estimation method comprises the following steps:
step 1, obtaining a parameter vector from formula (10) As an initial iteration value, the subscript l represents the first frequency point, and the superscript 0 represents the 0 th iteration;
The superscript T in the above formula represents matrix transposition, A l is a coefficient matrix at a frequency point f l, and I (n) represents an interference signal;
Step 2, obtaining a covariance matrix Γ κ by a formula (12), wherein the upper mark kappa represents the kappa-th iteration;
Wherein Q l is the covariance matrix corresponding to f l, For the amplitude frequency of the spectral peak frequency, A p is a coefficient matrix of the spectral peak frequency, p represents the p-th frequency point of the spectral peak, and L is the total number of frequency points in the interference amplitude frequency;
Step 3, obtaining the optimal parameter vector from the formula (14) The subscript κ represents the kth iteration;
Step 4, judging whether the preset iteration times are reached, if so, carrying out the next Step, otherwise, starting execution from Step 2;
step 5, estimating the optimal parameter vector as the iteration is completed Then the interference amplitude frequency/>, can be obtainedThe method comprises the following steps:
Wherein, The optimal parameter vector is the kappa-th iteration; the values X (f l), l=1, 2, & gt of the parameter vector at fl can be obtained by performing the above processing on all frequency pointsThe maximum likelihood estimation of vector X (f l) will be produced during the above-described Step 1 to Step 5 iterations, and as the iterations proceed, vector X (f l) and covariance matrix Γ will also converge gradually;
The interference frequencies f pk1 and f pk2 corresponding to the two spectral peaks are found in the interference amplitude frequency, the positions d pk1 and d pk2 corresponding to the spectral peaks are found, and the absolute value is taken, so that the optical thickness d int can be obtained:
dint＝|dpk1-dpk2 | (16)
Step 3, according to the confocal thickness d conf and the optical thickness d int, and combining the numerical aperture NA of the chromatic confocal probe, the geometric thickness d of the material can be obtained according to the following formula by combining the results, and then the refractive index n 2 can be obtained according to the formula (1):
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