An Algorithm for Inverse Calculation of Cavity Length in Multi-Surface Interferometry

Abstract

The present invention discloses a cavity length back-calculation algorithm in multi-surface interference measurement. The algorithm includes a method of independent sampling of frequency peaks, a method of back-calculating the cavity length by folding frequency sampling, and a method of back-calculating the cavity length of the head period. By analyzing the light intensity data obtained under multiple different samplings, the cavity lengths of each interference harmonic in multi-surface measurement can be accurately back-calculated. This algorithm is easy to implement, has a low technical difficulty, is novel in method, and has a high calculation accuracy.

Description

Technical Field

[0001] The present invention relates to an algorithm for back-calculating the cavity length in multi-surface interference measurement, especially a method for accurately back-calculating the cavity length in current multi-surface wavelength-shifting interference measurement through spectrum analysis, and is applied in the field of high-precision optical interference measurement. Background Art

[0002] Due to its high-quality surface height distribution and high parallelism, the optical flat is widely used in the design and construction of optical systems. If the surface height distribution of the optical flat does not meet the preset requirements, it may cause damage to the optical components in the system. Therefore, it is very important to detect the surface topography height of the optical flat during the processing.

[0003] Optical detection methods have high detection accuracy (up to the nanometer level). The general process of the phase-shifting interference measurement method can be divided into: placing the measured object at a certain distance in front of the interferometer, performing phase shifting with a certain phase shift value and taking the interference patterns during the phase shifting process, and processing the interference patterns to reconstruct the height information of the measured surface. When the parallelism of the front and back surfaces of the measured object is not high, the collected interference patterns are only the interference light intensity information between a single measured surface and the reference surface in the interferometer. However, once the measured object is an optical flat with high parallelism between the front and back surfaces, the collected interference pattern information is the result of the superposition of three groups of interference, namely, between the reference surface and the front measured surface, between the reference surface and the back measured surface, and between the front and back measured surfaces, and cannot be processed using traditional methods.

[0004] The wavelength-shifting interference measurement technology performs phase shifting operations by changing the wavelength of the light source. This phase shifting method can avoid problems such as mechanical hysteresis errors in traditional hardware phase shifting. And since only the wavelength of the light source is changed, when processing the interference pattern information of multiple superimposed surfaces, the topography of each surface of the measured object can be reconstructed based on the differences in the optical path differences in the optical system.

[0005] In addition, an important application of the wavelength-tuning phase-shifting interference technology is to calculate the measurement distances of each measured surface (the distances from each measured surface to the reference surface in the interferometer) and the optical thickness of the measured object (the product of the physical thickness of the measured object and the refractive index), which helps to monitor and feedback various important parameters during the measurement process. However, the current wavelength-shifting interference measurement algorithms are difficult to achieve this goal adaptively, and even the calculation results may completely fail.

[0006] Among multiple interferograms acquired during the phase shift process, if the pixel at a certain point on the interferogram is taken as the observation angle, the light intensity change of this pixel point at different frame numbers follows the form of a cosine function. In multi-surface interference measurement, the light intensity change of a single pixel point presents the form of superposition of three cosine harmonics with different frequencies, and the key factors determining the harmonic frequencies are the interference cavity lengths and wavelength tuning amounts of each harmonic. Specifically, the harmonic frequency determining the interference harmonic signal of thickness change is the optical thickness of the measured object and the wavelength tuning amount; the harmonic frequency determining the interference harmonic signal of the front surface is the distance from the front surface of the measured object to the reference surface and the wavelength tuning amount; the harmonic frequency determining the interference harmonic signal of the back surface is the sum of the distance from the front surface of the measured object to the reference surface and the optical thickness of the measured object, and the wavelength tuning amount, these three main parameters. The optical thickness of the measured object, the distance from the front surface of the measured object to the reference surface, and the sum of the distance from the front surface of the measured object to the reference surface and the optical thickness of the measured object can be called the interference cavity lengths of each harmonic interference signal, or harmonic cavity lengths.

[0007] The current difficulty in cavity length calculation mainly lies in the difficulty of accurately calculating the interference cavity length, especially how to accurately determine and back-calculate the cavity lengths of each harmonic when there are adverse factors such as frequency shift (shifting from the second period of the spectrum to the first period) and under-sampling (the number of sampling points of each harmonic in a single sampling period is close to or less than 2). At the same time, since the interferometer needs to be placed on an anti-vibration platform (hereinafter referred to as the platform), the length of the platform and the corresponding measurement range should be taken into account in the formulation of the measurement plan.

[0008] The currently common method is to make a wide-range estimation of parameters such as the measurement distance of the measured object. For example, it is estimated that the distance is between X1 and X2, and then the cavity length can be back-calculated. However, this estimation method still requires first measuring the prior information such as the measurement distance (such as using a ruler to measure the distance from the front surface of the measured object to the reference surface), which will undoubtedly increase the measurement cost, and if this prior measurement is inaccurate, it will introduce additional measurement errors, which is not conducive to the requirements of high-precision measurement.

[0009] The present invention proposes a cavity length back-calculation algorithm in multi-surface interference measurement. By determining the relative height position of the spectral peak of the interferogram obtained after multiple tunings, the frequency shift and frequency folding are identified, so as to accurately back-calculate the tuning times and the cavity lengths of each harmonic. Summary of the Invention

[0010] To solve the problem of accurately calculating the cavity lengths of each harmonic under a free cavity length without relying on prior information, the present invention proposes an algorithm for back-calculating the cavity length in multi-surface interference measurement. By determining the relative height positions of the spectral peaks of the interference patterns obtained after multiple tunings, the identification of frequency shifting and frequency folding is achieved, thereby accurately back-calculating the number of tuning times and the cavity lengths of each harmonic. This method can overcome the problem that traditional multi-surface measurement methods are not applicable to the accurate back-calculation of harmonic cavity lengths under a free cavity length, and does not require the estimation of other prior information except for the optical thickness (including the cavity length estimated by parameters such as the measurement distance for the harmonic signals of the front and back surfaces), and can adaptively determine the optimal sampling frequency. This method is easy to implement, has a low technical difficulty, and is novel in approach.

[0011] The steps for calculating the cavity length in wavelength-shifting interferometric measurement can be briefly described as follows: changing the wavelength of the light source according to a certain wavelength tuning amount, and collecting interference patterns to obtain a certain number of frames of interference patterns (such as 50 frames, that is, 50 interference patterns); then, processing the collected interference patterns to obtain the frequencies of each harmonic interference signal; and back-calculating the harmonic cavity lengths through the obtained frequencies of each harmonic.

[0012] According to the above inventive concept, the present invention adopts the following technical solutions:

[0013] As a basis, first, the important parameters in multi-surface phase-shifting interference measurement are given:

[0014] Taking n1 as the refractive index of the measured part and T as the average thickness of the measured part, under the long-cavity length interference condition (which means that the optical thickness n1T of the measured part is less than the distance H between the reference mirror and the front surface of the measured part), for the thickness change signal, the front surface signal, and the back surface signal, the harmonic relative frequencies F = 1, M, M + 1, where M is the ratio of the distance between the reference mirror and the front surface of the measured part to the optical thickness of the measured part, that is, H / (n1T).

[0015] At the same time, the phase-shifting reference coefficient N is defined. N can determine that the single-step phase-shifting value of the fundamental frequency signal (the signal with the minimum harmonic frequency) is 2π / N. Therefore, for the thickness change signal, the front surface signal, and the back surface signal, their phase-shifting values are 2π / N, M(2π / N), and (M + 1)(2π / N) respectively.

[0016] The total number of phase-shifting frames set in this application is XN, where N is greater than or equal to 8. X can be selected according to requirements, X is greater than or equal to 1, and when N is an even number greater than or equal to 8, the decimal part of X can be selected as 0.5 or X is selected as an integer greater than or equal to 1; when N is an odd number greater than or equal to 8, X is an integer; when N is an integer multiple of 10, X is any integer greater than or equal to 1 or a non-integer with only one decimal place, so that XN is an integer.

[0017] Using the discrete-time Fourier transform (DTFT) algorithm for the interference signal can obtain an approximately continuous spectrum of the interference signal. Compared with the spectrum obtained by the traditional fast Fourier transform, this spectrum has a smaller frequency interval, so it is easier to overcome the problem of inaccurate determination of the frequency peak position caused by factors such as phase-shift error. Since the obtained DTFT spectrum is symmetric, the right half of the spectrum is taken for analysis. By searching according to the amplitude peaks (referred to as peaks for short) within this half of the spectrum and positioning the frequency values corresponding to the abscissa, the frequencies of each harmonic can be obtained.

[0018] Under the condition of long cavity length interference, the frequencies of each harmonic can be expressed as:

[0019]

[0020] In the above formula, the subscript m of the harmonic frequency vm, where m = 1, 2, 3, corresponds to the thickness change signal, the front surface signal, and the back surface signal respectively. (x, y) are the coordinates on the interference pattern. Since there is a high parallelism between the front and back surfaces of the measured part, and each measured surface is also parallel to the reference surface in the reference mirror, the harmonic frequencies at each coordinate position are the same, so (x, y) can be omitted. In the above formula, the single-step wavelength tuning amount is Δλ, and the starting wavelength of the laser is λ0. The phase shift value of the harmonic is the harmonic frequency vm multiplied by 2π. As described above, for the thickness change signal, the front surface signal, and the back surface signal, their phase shift values are 2π / N, M(2π / N), (M + 1)(2π / N) respectively. The continuous writing between each symbol represents a multiplication operation, such as XN represents the multiplication of X and N values.

[0021] As mentioned above, during the phase-shift process, due to the limited tuning frequency and tuning speed of the laser, the number of phase-shift frames set during actual measurement is usually small. For classical DFT calculations (including FFT), considering the symmetric distribution of the spectrum, the effective points in the frequency domain are actually half of the number of phase-shift frames. When there are factors such as phase-shift error, the true frequency of the light intensity signal will be hidden between the sampling spectral lines, which is the fence effect. When performing the DTFT operation, since the spectrum can be divided at a smaller interval, the interval of the obtained effective points is greatly reduced. The frequency domain variable ω is divided in the range [0, 2π] (k T = 0, 1, 2, …, M K , M K can be called the total encryption amount):

[0022]

[0023] Substituting the above formula into the discretized DTFT expression (unwindowed form), we can get:

[0024]

[0025] In the above formula, Z = XN, which is the total number of sampling frames; k is the number of phase shifts; j is the imaginary unit; e is the natural base; x(k) is the light intensity change of a certain pixel point at different frames, and its form after DTFT is X; denote X(ω) = X(k T ), and perform the variable substitution of the following formula:

[0026]

[0027] Then we can get:

[0028]

[0029] After the above processing, the direct expression form of the approximate continuous DTFT spectrum after the discrete light intensity signal sequence is divided by the MK points can be obtained:

[0030]

[0031] When performing the Fourier transform of the sequence, the effect is the best when the length of the encrypted sequence is a function of a power of 2. After obtaining the spectrum of the signal (performing the modulus calculation on the above formula), the corresponding frequencies of each harmonic sub-signal in the spectrum can be calculated through the frequency peak addressing method, and then the inverse calculation of the cavity length of each harmonic can be realized accordingly. In the obtained spectrum curve, the ordinate of the curve is the amplitude.

[0032] Since only half of the spectrum is selected, only the spectrum between 0 and π needs to be analyzed. Plot the spectrum lines between 0 and π, locate the abscissas of the peak positions of the three curves from left to right, and then the following calculations can be obtained according to the coordinates KP containing the abscissa positions of the 3 harmonic peaks:

[0033] KPλ0^2 / (4πΔλ), where ^ represents the power calculation of the exponential part, and λ0^2 represents the square of λ0.

[0034] The wavelength tuning amount for each phase shift (hereinafter referred to as the wavelength tuning amount) can be solved according to the following method:

[0035] Based on the thickness change signal, multiply both sides by 2π on the left and right sides, then replace 2π on the left side of the equation with 2π / N, and then calculate Δλ through the equation after variable substitution. The N value substituted at this time is denoted as N1.

[0036] However, in the above calculation process, many problems are likely to occur, which cannot be solved by traditional methods. For example, when M = 2 and N = 12, the three peaks in the spectrum at this time correspond to the thickness change, the front surface, and the back surface signals from left to right. However, when M = 10, the three peaks in the spectrum at this time correspond to the thickness change, the back surface, and the front surface signals from left to right. It can be seen that when M is greater than N / 2, the peak positions of the latter two signals change. At the same time, when M = 14 (14 = 2 + 12) and N = 12, due to the defect of the Fourier transform itself, the obtained spectrum is exactly the same as the spectrum when M = 2 and N = 12. It is impossible to effectively and accurately solve the cavity length only through the inverse calculation of the frequency.

[0037] In order to overcome the problem that prior information estimation is required in the cavity length algorithm of traditional wavelength-shifting interference measurement, from the perspective of DTFT near-continuous spectrum analysis, an algorithm for inverse calculation of cavity length in multi-surface interference measurement is proposed. This algorithm includes a method of independent peak sampling, a method of inverse calculation of cavity length with frequency sampling folding, and an inverse algorithm of cavity length for the head period.

[0038] The method of independent peak sampling is specifically described as follows: Calculate the wavelength tuning amount based on the current optical thickness of the measured part and the initial N1, and collect the interference pattern of the measured part with XN1 as the total number of sampling frames; Determine the number of spectrum peaks of the interference pattern collected with N1 as the initial parameter. The specific determination method is as follows: Perform DTFT calculation on the light intensity change of the image center pixel point (x0, y0) in different frames of each interference pattern collected with N1 as the parameter and draw a spectrum diagram. If the number of the maximum peaks in the spectrum at this time is 3, then use the light intensity change of the point (x0, y0) in different frames as the light intensity sequence for frequency solution; If the number of the maximum peaks in the spectrum at this time is not 3, then move the point (x0, y0) one unit to the upper right side of the image, and the new pixel position obtained is (x0 + 1, y0 + 1) = (x1, y1). Calculate the number of peaks in the spectrum after performing DTFT on (x1, y1) again. If the number of the maximum peaks in the spectrum at this time is 3, then use the light intensity change of the point (x1, y1) in different frames as the light intensity sequence for frequency solution. If the number of the maximum peaks in the spectrum at this time is not 3, then add 4 to N1 and cover the initially set N1 with the value of N1, and perform the above determination of the number of spectrum peaks again until the number of the maximum peaks in (x1, y1) or (x0, y0) is 3, and use the light intensity change in different frames as the light intensity sequence for frequency solution.

[0039] In the above description, adding 4 to N1 and covering the initially set N1 with the value of N1 is actually the common operation of N1 = N1 + 4 in programming. This description method is to prevent confusion with the variable meanings in the following text.

[0040] The specific description of the frequency sampling folding cavity length back-calculation method is as follows: The spectrum obtained after performing DTFT transformation on the light intensity sequence obtained by independent frequency peak sampling is used as the calculation target and denoted as A1. If the relative heights of the harmonic frequency peak heights in A1 arranged from left to right between 0 and π are the second highest value, the lowest value, and the highest value in turn, then current spectrum folding occurs. Essentially, the spectrum of the next period is folded into the first period for observation, or rather, the actual harmonic frequency peak is symmetrically folded about π into the spectrum of the observed first period (0 to π), and the value of the first element in the parameter vector JDM is assigned 2; if the relative heights of the harmonic frequency peak heights in A1 arranged from left to right between 0 and π are the second highest value, the highest value, and the lowest value in turn, then no spectrum folding occurs currently, and the value of the first element in the parameter vector JDM is assigned 1; after the value of the first element in the parameter vector JDM is assigned, with N2 = 2N1 as the initial parameter, the sampling frame number XN2 is calculated and the wavelength tuning amount is calculated to collect the interferogram again. The spectrum obtained using the frequency peak independent sampling method is denoted as A2. If the relative heights of the harmonic frequency peak heights in A2 arranged from left to right between 0 and π are the second highest value, the highest value, and the lowest value in turn, then the value of the second element in the parameter vector JDM is assigned 1, otherwise the value of the second element in the parameter vector JDM is assigned 2; if the value of the second element in JDM is assigned 2 and the value of the first element in JDM is assigned 1, then it is denoted as JZD = 1; if the value of the second element in JDM is assigned 1 and the value of the first element in JDM is assigned 2, then it is denoted as JZD = 2; if JZD = 1, then using A2 as the frequency peak positioning target, the corresponding cavity length values of the thickness change signal, the front surface signal, and the back surface signal are calculated by performing the calculation of KPλ0^2 / (4πΔλ) on the abscissa vector KP corresponding to the frequency peaks from left to right in A2; if JZD = 2, then using A2 as the frequency peak positioning target, at this time, the three values in the three abscissa KP vectors corresponding to the three frequency peaks from left to right in A2 are [KP0, KPA, KPB], and the KP vector is replaced with [KP0, (abs(2πKPA - π) + π) / (2π), (abs(2πKPB - π) + π) / (2π)], where abs represents the positive operation, and the following calculation is performed on the newly obtained vector KP: KPλ0^2 / (4πΔλ), thereby calculating the corresponding cavity length values of the thickness change signal, the front surface signal, and the back surface signal.

[0041] If the values of two adjacent elements in the obtained vector JDM are different, there is no need to perform phase shift and frequency peak independent sampling again; if the values of two adjacent elements in the vector JDM are the same, continue with frequency peak independent sampling until the values of two adjacent elements in JDM are different; when the values of two adjacent elements are different and the number of times J of frequency peak independent sampling is greater than or equal to 3 times, and at this time the value of the last element in JDM is 2, calculate the cavity length value using the A1 spectrum, calculate KPλ0^2 / (4πΔλ) for the abscissa vector KP corresponding to the frequency peaks from left to right in A1 to obtain the cavity length primary inversion values of the thickness change signal, the front surface signal, and the back surface signal, and denote them as CL1(1), CL1(2), and CL1(3) respectively. Then, add J times the thickness change signal primary inversion value CL1(1) to the front surface cavity length primary inversion value CL1(2) among the solved cavity length primary inversion values to obtain CL2(2), add J times the thickness change signal primary inversion value CL1(1) to the back surface cavity length primary inversion value CL1(3) among the solved cavity length primary inversion values to obtain CL2(3), and assign CL2(1) = CL1(1). At this time, the obtained CL2(1), CL2(2), and CL2(3) are the accurate cavity length values of each harmonic.

[0042] The specific description of the head period cavity length inversion algorithm is as follows: if the value of J is greater than or equal to 4 and the values of all elements in JDM are 1, it is determined that the current cavity length coefficient M is between 0 and N1, where M is the ratio of the distance between the front surfaces of the measured part to the optical thickness of the measured part. Then, calculate the cavity length value using the A1 spectrum, and calculate KPλ0^2 / (4πΔλ) for the abscissa vector KP corresponding to the frequency peaks from left to right in A1 to obtain the cavity length values of the thickness change signal, the front surface signal, and the back surface signal.

[0043] The applicable range of the cavity length inversion algorithm in the multi-surface interference measurement is M = 2 to 2.5N1, the thickness T of the measured part is greater than 1 mm, and the number of interference fringes of each harmonic is less than 40.

[0044] The present invention proposes a cavity length inversion algorithm in multi-surface interference measurement. By determining the relative height position of the spectral peak of the interference pattern obtained after multiple tunings, it realizes the identification of frequency shifting and frequency folding, thereby accurately inverting the number of tuning times and the cavity length of each harmonic. Compared with the prior art, the advantages of the present invention are as follows:

[0045] (1) It can realize the adaptive calculation of the cavity length of each harmonic at any cavity length without the need for prior information such as measurement distance.

[0046] (2) There is no strict limit on the platform length during measurement, and accurate cavity length inversion can be achieved within a wide measurement range.

[0047] (3) It can achieve adaptive multiple tuning, and there is no need to rotate the measured part and manually input and determine the calculation parameters during the measurement process. Description of the Drawings

[0048] The present invention will be further described below in conjunction with the drawings and example processes.

[0049] Figure 1 is a spectrogram;

[0050] Figure 2 is a schematic diagram of a wavelength tuning phase-shifting interferometer;

[0051] Figure 3 is a schematic diagram of the harmonic superposition of each interference signal observed at a single pixel point under different frame numbers;

[0052] Figure 4 is a schematic diagram of the harmonic superposition of each interference signal observed from the entire interference pattern. Detailed Embodiment

[0053] In order to overcome the problem that prior information estimation is required for the cavity length algorithm in traditional wavelength phase-shifting interference measurement, from the perspective of DTFT near-continuous spectrum analysis, an algorithm for back-calculating the cavity length in multi-surface interference measurement is proposed. This algorithm includes a method of independent sampling of frequency peaks, a method of back-calculating the cavity length by folding frequency sampling, and a method of back-calculating the cavity length of the head period.

[0054] The preferred embodiments of the present invention are described in detail below in conjunction with the drawings:

[0055] Embodiment 1:

[0056] According to Figure 1 in the drawings, after performing DTFT calculation on the light intensity change of a single pixel point and extracting the spectrum, an approximately continuous curve can be obtained. The frequencies of different signals can be extracted according to the positions of each peak, and the cavity length can be back-calculated according to the relationship between the signal frequency and the cavity length of each harmonic interference.

[0057] According to Figure 2 in the drawings, it can be seen that each harmonic signal has a different frequency. Combining Figure 3 , this difference in harmonic signal frequency comes from the different interference cavity lengths of each harmonic. According to Figure 3 and Figure 4 it can be seen that from the perspective of a single pixel point, during multi-surface wavelength tuning phase-shifting interference measurement, the intensity change of the interference light intensity under different frame numbers follows the form of the superposition of three cosine functions with different frequencies, and this superposition characteristic can also be observed on the entire interference pattern.

[0058] Since each harmonic frequency depends not only on the interferometric cavity length but also on the single-step wavelength tuning amount. Therefore, when calculating the interferometric cavity length of harmonics, it should first be ensured that each harmonic frequency is significantly different. From the perspective of the spectrum, the frequency peaks of each harmonic signal should be independent of each other, without the situation of too close frequency peaks or the superposition of two frequency peaks. In addition, the peak height (amplitude) of each harmonic in the spectrum depends on the behavior of the laser beam passing through the measured part and reflecting from each surface in the interferometer, which will determine the peak height of each harmonic signal. According to the analysis of each beam in the interferometer, the amplitude of the front surface interference signal is the highest, the amplitude of the back surface interference signal is the lowest, and the amplitude of the thickness change signal is between the amplitude heights of the above two, which provides a basis for the automatic determination of frequency peak attribution.

[0059] The method of independent sampling of frequency peaks is specifically described as follows: Calculate the wavelength tuning amount based on the current optical thickness of the measured part and the initial N1 calculation wavelength, and collect the interference pattern of the measured part with XN1 as the total number of sampling frames; Determine the number of spectrum peaks of the interference pattern collected with N1 as the initial parameter. The specific determination method is as follows: Perform DTFT calculation on the light intensity change of the image center pixel point (x0, y0) in different frames of each interference pattern collected with N1 as the parameter and draw a spectrum diagram. If the number of the maximum peak amplitudes in the spectrum is 3 at this time, then use the light intensity change of the point (x0, y0) in different frames as the light intensity sequence for frequency solution; If the number of the maximum peaks in the spectrum is not 3 at this time, then move the point (x0, y0) one unit to the upper right side of the image, and the new pixel position obtained is (x0 + 1, y0 + 1) = (x1, y1). Calculate the number of frequency peaks in the spectrum after performing DTFT on (x1, y1) again. If the number of the maximum frequency peaks in the spectrum is 3 at this time, then use the light intensity change of the point (x1, y1) in different frames as the light intensity sequence for frequency solution. If the number of the maximum frequency peaks in the spectrum is not 3 at this time, then add 4 to N1 and cover the initially set N1 with the value of N1, and perform the above determination of the number of spectrum peaks again until the number of the maximum frequency peaks in (x1, y1) or (x0, y0) is 3, and use the light intensity change in different frames as the light intensity sequence for frequency solution.

[0060] In the above description, adding 4 to N1 and overriding the initially set value of N1 is actually the common operation of N1 = N1 + 4 in programming. This description method is to prevent confusion with the variable meanings in the following text. In other words, essentially N is equivalent to the sampling frequency. Starting from the spectrum of the light intensity change of a single pixel point, if a spectrum with three independent peaks cannot be solved for this point, it may be due to interference signal contamination caused by dirty points in the interferometer system or the interferogram acquisition device. Therefore, move to another pixel and analyze again. If spectra with three independent peaks cannot be solved for multiple pixel points, the reason for this bad situation is that the set value of the sampling frequency N cannot meet the current requirements. Therefore, the countermeasure is to change the value of N and sample again.

[0061] The described method for inverse calculation of the frequency-sampling folded cavity length is specifically described as follows: The spectrum obtained by performing DTFT transformation on the optical intensity sequence obtained through independent frequency-peak sampling is used as the calculation target and denoted as A1. If the relative heights of the harmonic frequency peaks in A1 arranged from left to right between 0 and π are the second-highest value, the lowest value, and the highest value in sequence, then current spectrum folding occurs, and the value of the first element in the parameter vector JDM is assigned 2; if the relative heights of the harmonic frequency peaks in A1 arranged from left to right between 0 and π are the second-highest value, the highest value, and the lowest value in sequence, then current spectrum folding does not occur, and the value of the first element in the parameter vector JDM is assigned 1; after the value of the first element in the parameter vector JDM is assigned, with N2 = 2N1 as the initial parameter, calculate the number of sampling frames XN2 and calculate the wavelength tuning amount, and then perform interferogram acquisition again. The spectrum obtained using the described independent frequency-peak sampling method is denoted as A2. If the relative heights of the harmonic frequency peaks in A2 arranged from left to right between 0 and π are the second-highest value, the highest value, and the lowest value in sequence, then the value of the second element in the parameter vector JDM is assigned 1, otherwise the value of the second element in the parameter vector JDM is assigned 2; if the value of the second element in JDM is assigned 2 and the value of the first element in JDM is assigned 1, then denote it as JZD = 1; if the value of the second element in JDM is assigned 1 and the value of the first element in JDM is assigned 2, then denote it as JZD = 2; if JZD = 1, then use A2 as the frequency-peak positioning target, and calculate the corresponding cavity length values of the thickness change signal, the front surface signal, and the back surface signal by performing the calculation of KPλ0^2 / (4πΔλ) on the abscissa vector KP corresponding to the frequency peaks from left to right in A2; if JZD = 2, then use A2 as the frequency-peak positioning target. At this time, the three values in the abscissa KP vector corresponding to the three frequency peaks from left to right in A2 are [KP0, KPA, KPB], and replace the KP vector with [KP0, (abs(2πKPA - π) + π) / (2π), (abs(2πKPB - π) + π) / (2π)], where abs represents the positive operation, and perform the following calculation on the newly obtained vector KP: KPλ0^2 / (4πΔλ), thereby calculating the corresponding cavity length values of the thickness change signal, the front surface signal, and the back surface signal.

[0062] The core of the method described above lies in that if the relative height position of the peak in the spectrum changes under different N values, then it can be basically determined where the actual signal frequency is located, and thus the cavity length can be inversely calculated. When using the DTFT method for spectrum analysis, the following characteristics exist in multi-surface wavelength-shifting interferometric measurement: when M = 2 to N / 2, the spectrum does not fold; when M = N / 2 to N, the spectrum folds. The above method and the method in Embodiment 2 are both proposed based on this. As an example, if M = 8 and N = 12 at this time, the spectrum after this sampling has folded, so sampling is performed with N = 24 (2 times of 12). At this time, M = 8 and N = 24, and the spectrum is normally distributed (does not fold) at this time. Based on this, it is determined that M is in the section of M = N / 2 to N, and the cavity length can be inversely calculated according to the peak corresponding frequency values in the spectra of the two samplings.

[0063] Meanwhile, if spectrum folding occurs, combined with Figure 1 , at this time, the actual frequency peaks of the front surface signal and the rear surface should be folded between π and 2π with π as the axis of symmetry, but the sampled spectrum is symmetric about -π to π, and the spectrum between π and 2π cannot be observed. Therefore, only the frequency peaks and the abscissa corresponding frequencies folded between 0 and π in the spectrum can be used to inversely calculate the real frequency.

[0064] In the specific description of the above-introduced frequency sampling folding cavity length inverse calculation method, there is also a corresponding example. Starting from the actual distance, when M is between (2N + 2) and 2.5N, the situation where JDM(1) ((1) represents the first element in JDM) is 1 and JDM(2) is 2 will occur. When M = 14 and N = 12, it can be found by drawing the spectrum of the sampled light intensity at this time that there is no frequency folding currently. When N is increased to 24, frequency folding occurs at this time, and the specific value of M can be accurately inversely calculated based on this characteristic.

[0065] Embodiment 2:

[0066] If the values of two adjacent elements in the obtained vector JDM are different, there is no need to perform phase shift and frequency peak independent sampling again; if the values of two adjacent elements in the vector JDM are the same, continue with frequency peak independent sampling until the values of two adjacent elements in JDM are different; when the values of two adjacent elements are different and the number of times J of frequency peak independent sampling is greater than or equal to 3 times, and at this time the value of the last element in JDM is 2, calculate the cavity length value using the A1 spectrum, calculate KPλ0^2 / (4πΔλ) for the abscissa vector KP corresponding to the frequency peaks from left to right in A1 to obtain the cavity length first inversion values of the thickness change signal, the front surface signal, and the back surface signal, and denote them as CL1(1), CL1(2), and CL1(3) respectively. Then, add J times the first inversion value of the thickness change signal CL1(1) to the first inversion value of the front surface cavity length CL1(2) among the solved cavity length first inversion values to obtain CL2(2), add J times the first inversion value of the thickness change signal CL1(1) to the first inversion value of the back surface cavity length CL1(3) among the solved cavity length first inversion values to obtain CL2(3), and assign CL2(1) = CL1(1). At this time, the obtained CL2(1), CL2(2), and CL2(3) are the accurate cavity length values of each harmonic.

[0067] The specific description of the head periodic cavity length inversion algorithm is as follows: If the value of J is greater than or equal to 4 and all the element values in JDM are 1, it is determined that the current cavity length coefficient M is between 0 and N1, where M is the ratio of the distance between the front surfaces of the measured part to the optical thickness of the measured part. Then, calculate the cavity length value using the A1 spectrum, and calculate KPλ0^2 / (4πΔλ) for the abscissa vector KP corresponding to the frequency peaks from left to right in A1 to obtain the cavity length values of the thickness change signal, the front surface signal, and the back surface signal.

[0068] The core of the method described above is as follows: If sampling is performed multiple times at different frequencies and the relative height positions of the peaks in the light intensity spectrum after each sampling do not change under different N values, then it can be basically determined where the actual signal frequency is located. Currently, it meets M = 2 to N / 2, and thus the cavity length can be inversely calculated. For example, if M = 2 and N = 12, at this time the spectrum is normally distributed (without folding). Increase N to 24 and perform spectrum analysis again. The spectrum is still normally distributed (without folding). Performing this kind of sampling and spectrum analysis multiple times will find that the spectrum is always normally distributed. Therefore, it can be determined that M = 2 to N / 2, and thus the cavity length can be accurately inversely calculated.

[0069] The applicable range of the cavity length inversion algorithm in the multi-surface interference measurement is M = 2 to 2.5N1, the thickness T of the measured part is greater than 1 mm, and the number of interference fringes of each harmonic is less than 40.

[0070] From the attached drawings Figure 4As can be seen, due to the undulating changes in the surface shape of the device under test, the collected fringe pattern is actually a series of concentric circles or individual stripes. If the darkest part is counted as one fringe, then the fewer the number of fringes, the flatter the surface undulation, which is beneficial to the progress of interference measurement.

[0071] The above has described the embodiments of the present invention in conjunction with the accompanying drawings. However, the present invention is not limited to the above embodiments and can be subject to various changes according to the purpose of the invention. Any changes, modifications, substitutions, combinations, or simplifications made based on the spirit and principle of the technical solution of the present invention shall be equivalent replacement methods. As long as they meet the purpose of the present invention and do not deviate from the technical principle and inventive concept of the present invention, they all fall within the protection scope of the present invention.

Claims

1. A cavity length back-calculation algorithm in multi-surface interference measurement, the algorithm includes a method of independent sampling of frequency peaks, a method of back-calculating cavity length by folding frequency sampling, and a method of back-calculating cavity length for the head period; The method of independent sampling of frequency peaks is specifically described as follows: Calculate the wavelength tuning amount based on the current optical thickness of the measured part and the initial N1, and collect the interference pattern of the measured part with XN1 as the total number of sampling frames; Determine the number of spectral peaks of the interference pattern collected with N1 as the initial parameter. The specific determination method is as follows: Perform DTFT calculation on the light intensity changes of the image center pixel point (x0, y0) in different frames of each interference pattern collected with N1 as the parameter and draw a spectrogram. If the number of the maximum peaks in the spectrum at this time is 3, then use the light intensity changes of the point (x0, y0) in different frames as the light intensity sequence for frequency solution; If the number of the maximum peaks in the spectrum at this time is not 3, then move the point (x0, y0) one unit to the upper right side of the image, and the new pixel position obtained is (x0 + 1, y0 + 1) = (x1, y1). Calculate the number of frequency peaks in the spectrum after performing DTFT on (x1, y1) again. If the number of the maximum frequency peaks in the spectrum at this time is 3, then use the light intensity changes of the point (x1, y1) in different frames as the light intensity sequence for frequency solution. If the number of the maximum frequency peaks in the spectrum at this time is not 3, then add 4 to N1 and cover the initially set N1 with the value of N1, and perform the above determination of the number of spectral peaks again until the number of the maximum frequency peaks in (x1, y1) or (x0, y0) is 3, and use the light intensity changes of (x1, y1) or (x0, y0) in different frames as the light intensity sequence for frequency solution; The specific description of the frequency sampling folding cavity length back-calculation method is as follows: The spectrum obtained by performing DTFT transformation on the light intensity sequence obtained by independent frequency peak sampling is used as the calculation target and denoted as A1. If the relative heights of the harmonic frequency peak heights in A1 from left to right between 0 and π are the second highest value, the lowest value, and the highest value in sequence, then current spectrum folding occurs, and the value of the first element in the parameter vector JDM is assigned 2; if the relative heights of the harmonic frequency peak heights in A1 from left to right between 0 and π are the second highest value, the highest value, and the lowest value in sequence, then current spectrum folding does not occur, and the value of the first element in the parameter vector JDM is assigned 1; after the value of the first element in the parameter vector JDM is assigned, with N2 = 2N1 as the initial parameter, the sampling frame number XN2 is calculated and the wavelength tuning amount is calculated, and then the interferogram is collected again. The spectrum obtained by using the frequency peak independent sampling method is denoted as A2. If the relative heights of the harmonic frequency peak heights in A2 from left to right between 0 and π are the second highest value, the highest value, and the lowest value in sequence, then the value of the second element in the parameter vector JDM is assigned 1, otherwise the value of the second element in the parameter vector JDM is assigned 2; if the value of the second element in JDM is assigned 2 and the value of the first element in JDM is assigned 1, then JZD = 1 is recorded; if the value of the second element in JDM is assigned 1 and the value of the first element in JDM is assigned 2, then JZD = 2 is recorded; if JZD = 1, then using A2 as the frequency peak positioning target, the corresponding cavity length values of the thickness change signal, the front surface signal, and the back surface signal are calculated by performing the calculation of KPλ0^2 / (4πΔλ) on the abscissa vector KP containing the frequency peaks from left to right in A2; if JZD = 2, then using A2 as the frequency peak positioning target, at this time, the three values in the abscissa KP vector corresponding to the three frequency peaks from left to right in A2 are [KP0, KPA, KPB], and the KP vector is replaced with [KP0, (abs(2πKPA - π) + π) / (2π), (abs(2πKPB - π) + π) / (2π)], where abs represents the positive operation, and the following calculation is performed on the newly obtained vector KP: KPλ0^2 / (4πΔλ), thereby calculating the corresponding cavity length values of the thickness change signal, the front surface signal, and the back surface signal. The specific description of the head cycle cavity length back-calculation method is as follows: If the value of J is greater than or equal to 4 and all the element values in JDM are 1, then it is determined that the current cavity length coefficient M is between 0 and N1, where M is the ratio of the distance between the front surfaces of the measured part to the optical thickness of the measured part. Then, the cavity length value is calculated using the A1 spectrum, and the corresponding cavity length values of the thickness change signal, the front surface signal, and the back surface signal are calculated by performing the calculation of KPλ0^2 / (4πΔλ) on the abscissa vector KP containing the frequency peaks from left to right in A1.

2. The cavity length back-calculation algorithm in multi-surface interference measurement according to claim 1, wherein: The applicable range of the cavity length back-calculation algorithm in the multi-surface interference measurement is M = 2 - 2.5N1, the thickness T of the measured part is greater than 1 mm, and the number of interference fringes of each harmonic is less than 40.

3. The frequency sampling folding cavity length back-calculation method in the cavity length back-calculation algorithm for multi-surface interference measurement according to claim 1, wherein: If the values of two adjacent elements in the obtained vector JDM are different, there is no need to perform phase shift and frequency peak independent sampling again; if the values of two adjacent elements in the vector JDM are the same, continue with frequency peak independent sampling until the values of two adjacent elements in JDM are different; when the values of two adjacent elements are different and the number of times J of frequency peak independent sampling is greater than or equal to 3 times, and at this time the value of the last element in JDM is 2, calculate the cavity length value using the A1 spectrum, calculate KPλ0^2 / (4πΔλ) for the abscissa vector KP corresponding to the frequency peaks from left to right in A1 to obtain the first cavity length inverse calculation values of the thickness change signal, the front surface signal, and the back surface signal, denoted as CL1(1), CL1(2), and CL1(3) respectively. Then, add J times the first cavity length inverse calculation value of the thickness change signal CL1(1) to the first cavity length inverse calculation value of the front surface CL1(2) among the solved first cavity length inverse calculation values to obtain CL2(2), add J times the first cavity length inverse calculation value of the thickness change signal CL1(1) to the first cavity length inverse calculation value of the back surface CL1(3) among the solved first cavity length inverse calculation values to obtain CL2(3), and assign CL2(1) = CL1(1). At this time, the obtained CL2(1), CL2(2), and CL2(3) are the cavity length values of each harmonic.

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