CN114964033A - Method for measuring super-surface topography distribution by using wavelength phase-shifting method - Google Patents
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Abstract
The invention discloses a method for measuring super-surface topography distribution by using a wavelength phase-shifting method. The method comprises the following operation steps: acquiring and processing an interference pattern on the super surface by using a wavelength phase-shifting interference technology: phase-shifting acquisition and weighted averaging processing of the interferogram, screening an effective area of the interferogram, and removing background noise from the interferogram. Correcting the phase shift value based on time domain discrete Fourier transform: extracting characteristic signals of the interference pattern, eliminating invalid characteristic signals based on multipoint time domain illumination cross-correlation coefficients, and solving phase shift frequency through time domain Fourier transform. The method has the advantages of simple algorithm, small calculated amount and high solving precision, and has very important significance for measuring the super surface with high precision.
Description
Technical Field
The invention relates to a method for measuring super-surface topography distribution, in particular to a method for measuring super-surface topography distribution by using a wavelength phase-shifting method. Namely a method for carrying out interferogram acquisition processing and phase-shifting frequency correction based on time domain discrete Fourier transform development by using a wavelength tuning phase-shifting method.
Background
The method for recovering and reconstructing the surface topography of a measured piece by using an optical technology and an optical principle is a non-contact measuring method. The measurement algorithm developed based on the optical detection technology can realize high-precision measurement of the measured surface, and the precision can reach nanometer or even sub-nanometer level.
The super surface can realize effective regulation and control of characteristics such as electromagnetic wave polarization, amplitude, propagation mode and the like, and is widely applied in the optical and electronic fields. Such surfaces are typically distributed with columnar features on the order of hundreds of nanometers in height, and such super surfaces are traditionally measured using white light interferometry. However, white light interferometry has significant drawbacks:
(1) the algorithm is relatively complex to realize;
(2) the algorithm precision is not high;
(3) the method of solving pixel by pixel has higher calculation cost in industrial detection.
Phase-shifting interferometry is a high-precision detection technique. Based on the technology, a series of interferograms with different phases (after phase shifting) are collected through an interferometer, the solution of the phase distribution of the measured surface can be realized by calculating the interference light intensity distribution in the collected interferograms through a related phase demodulation algorithm, and therefore the measured surface is reconstructed through the linear relation between the phase and the surface appearance distribution. Traditionally, phase-shifting interference is the phase-shifting operation of interference intensity signals of a measured surface by pushing a reference mirror in an interferometer through a mechanism equipped with piezoelectric ceramics. However, this approach has limitations in that: (1) when the piezoelectric ceramic mechanism is used for pushing the reference mirror, inevitable stress errors and mechanical hysteresis errors can be generated; (2) when a large-caliber measured piece is measured, the matched reference mirror has a larger caliber, and the large-mass reference mirror can increase the mechanical hysteresis error of the reference mirror, so that the phase shift is not accurate, and the measurement accuracy is finally reduced.
Disclosure of Invention
In order to solve the problems of the prior art, the invention aims to overcome the defects in the prior art, and provides a method for measuring the super-surface morphology distribution by using a wavelength phase-shifting method, so as to realize high-precision measurement of the super-surface.
In order to achieve the aim of the invention, the conception of the invention is as follows:
the wavelength tuning phase-shifting interferometry can realize the phase change of a detected wave surface by changing the wavelength of an output light source of a laser, thereby realizing the phase-shifting operation. In the phase shifting process, only the voltage (temperature or current) applied to the laser needs to be controlled, and hardware such as a reference mirror does not need to be moved, so that the phase shifting method has high phase shifting precision, and high-precision surface measurement can be realized. In addition, the method can adjust and calculate the phase shift value according to the optical path difference of the measured surface to the reference mirror and the wavelength tuning quantity. In the process, the traditional algorithm usually performs Taylor expansion on a phase value based on an estimated value of the cavity length and the optical thickness of the measured element, and calculates a phase shift value in a low-order term mode.
The proposed technique is directed to a measurement object that is a super-surface with a surface distributed with nano-pillar structures. The surface topography is reconstructed by acquisition of a series of interferograms and phase demodulation using the proposed algorithm. In the process of acquiring the interferogram, in order to reduce the adverse effect of adverse factors such as vibration on a measurement result, the interferogram is solved and recorded in a multi-frame interferogram weighted average mode, and the acquired interferogram is stored in a computer for subsequent processing. In order to effectively reduce the adverse effect of the invalid measurement region on the solution result, the effective region extraction operation is carried out on the interference pattern by using the analysis code matrix with the numerical value only containing 0 or 1. In order to reduce the adverse effect of background components and background noise which is difficult to completely eliminate on the measurement result, an interferogram acquisition method with the sequence length of 2N +3 (wherein N is the number of phase-shifting divisions, and the phase-shifting value can be determined to be 2 pi/N) is adopted in interferogram acquisition, namely 2 whole periods of interference intensity signals are acquired and 3 frames of interferograms are added, and the interferograms are segmented for description. Wherein the frame number is [1:1:2N ] (taking the 1 st frame interferogram as the initial, the 1 st frame interferogram as the step length, the 2N frame interferogram as the final value, and the following expression meaning is the same) as the first section interferogram, the frame number is [2:1:2N +1] as the second section interferogram, and the frame number is [3:1:2N +3] as the third section interferogram. Therefore, the 2N +3 frame interferogram is divided into three sections, the initial interferogram frame number is sequentially staggered to be 1, and the total frame number of each section is 2N frames. And after solving the respective light intensity average value of each section of the interference image, carrying out averaging processing again so as to realize the calculation of the background component and the additive noise of the interference image. And taking the first section of interferogram (the frame number distribution is [1:1:2N ]) as a subsequent main measurement interferogram object, and subtracting the background component and the additive noise obtained by the calculation from each frame of interferogram so as to eliminate the influence of the two adverse factors on a solution result. In order to accurately solve the phase shift value and overcome the influence of abnormal noise data on a solving result, an abnormal data removing method based on a multipoint time domain illumination intensity cross-correlation function is designed, and an expanded Fourier transform algorithm is constructed.
According to the inventive concept, the invention adopts the following technical scheme:
a method for measuring super-surface topography distribution by using a wavelength phase shift method is characterized by comprising the following operation steps:
(1) acquiring and processing an interference pattern on the super surface by using a wavelength phase-shifting interference technology:
(1-1) phase-shifting acquisition and weighted averaging processing of an interference pattern;
(1-2) screening an effective area by using an interferogram;
(1-3) removing background noise from the interferogram;
(2) correcting the phase shift value based on time domain discrete Fourier transform:
(2-1) extracting characteristic signals of the interferogram;
(2-2) eliminating invalid characteristic signals based on the multipoint time domain illumination cross correlation coefficient;
and (2-3) solving the phase shift frequency by time domain Fourier transform.
The main implementation flow of the method of the invention can be summarized as follows:
(1) and (4) establishing and realizing an interferogram acquisition scheme. Collecting an interference pattern on the super surface with the nano-pillar structure by using a wavelength tuning phase-shifting interferometer; the phase shift times of the interferogram is 2N +3, N being integerThe number or decimal part is a non-integer of 0.5, and the total acquisition frame number is 5 (2N +3), namely the acquisition frame number of the interferogram after each phase shift is 5; and (3) carrying out weighted average processing on the 5 frames of interferograms after each phase shifting, and taking the processed interferograms as the interferograms after the current phase shifting, thereby finally obtaining 2N +3 frames of phase shifting interferograms. And (3) recording light intensity data of the k-th phase-shifting interferogram as I (k), wherein k is 1-2N +3, and k is an integer. The pixel sizes in the transverse and longitudinal directions of the interference pattern are respectively marked as X T 、Y T ；
(2) And setting an analysis code of the effective measurement area and solving a background value. The analysis code is 1 matrix, the size of the matrix is consistent with that of the interference pattern, wherein the value of the effective area is set to be 1, and the value of the ineffective area is set to be 0. And performing dot multiplication operation on each frame of interference image and the analysis code before subsequent processing, wherein the obtained result interference image participates in subsequent calculation. And carrying out segmentation solving on the 2N +3 frames of interferograms multiplied by the analysis code points to obtain background values including background components and additive noise, and averaging the background values obtained by each segment to be used as the basis of subsequent background removing operation. The number of the segments is 3, the 1 st frame to the 2N frame are taken as the first segment, the initial frame numbers of the 3 segments of the interferogram are sequentially staggered to be 1, and the total frame numbers of the segments are 2N frames;
(3) and (4) performing interference pattern de-averaging operation. Subtracting the background value obtained after the averaging processing from the first section of interference image obtained after the analysis code processing in the previous step to obtain an interference image which is similar to the pure background, wherein the pure interference image is called as I' (k) hereinafter, and the value range of the k value is 1-2N at the moment;
(4) and extracting the characteristic signal. Taking the 2N frame pure interferogram obtained in the previous step as the image center point (X) 0 ，Y 0 ) The light intensity data of the adjacent 9 positions of the point in the effective area are extracted as the geometric center. 2N light intensity data sequences can be constructed by arranging and counting the extraction points of each frame of interferogram from left to right and then from top to bottom, and are represented as
Wherein i is 1-9, and is recorded as a characteristic signal sequence in the kth light intensity data sequenceIth element I' k (i) Representing an ith characteristic signal extracted from the k frame pure interference image;
(5) calculating the weighted average value of each characteristic signal sequence as I U ' (k) and calculating a characteristic signal I ' in each characteristic signal sequence ' k (i) Weighted mean value I corresponding thereto U '(k) Cross-correlation coefficient H' k (i) And constructing a sequence of cross-correlation coefficients as
(6) And eliminating invalid characteristic signals through the distribution characteristics of the cross-correlation coefficients. Performing in-sequence descending, namely, arranging from large to small, on the cross-correlation coefficient sequences obtained by the previous step, selecting the maximum value and the minimum value of the cross-correlation coefficient sequences, removing the characteristic signals corresponding to the two values, thus remaining 7 characteristic signals in each characteristic signal sequence, and then performing equalization processing on each characteristic signal sequence after data removal to obtain 2N pieces of light intensity data, which are marked as I' aver (k) And using the interference pattern as an element to obtain an equalization sequence of each interference pattern
(7) Averaging sequences for each interferogram
And carrying out expanded Fourier transform. Will be provided with
Combining with a sequence, namely a vector, composed of zero values with the length of 6N to form a sequence to be analyzed
Wherein m is 1-8N,
the sequence length of (a) is 6N, all internal elements are 0, and q is an integer distributed in 1-6N. To pair
And performing discrete Fourier transform to obtain the frequency spectrum distribution formed by the frequency and the amplitude. In the obtained frequency spectrum distribution, the amplitudes corresponding to the frequencies are arranged in a descending order, and the frequency corresponding to the maximum amplitude value is selected and recorded as the rough selection phase-shifting frequency. And solving a frequency mean value for 2 frequency points adjacent to the roughly selected phase shifting frequency in the frequency spectrum, dividing the sum of the values of the 2 frequency points by 2, and recording the obtained result as the roughly corrected phase shifting frequency. The roughly selected phase-shifting frequency and the roughly corrected phase-shifting frequency are solved to obtain a frequency mean value, the sum of the values of the 2 frequency points is divided by 2, and the obtained result is recorded as the phase-shifting correction frequency f 0 ；
(8) The initial phase of the signal is solved by using a window function and a phase shift correction frequency. Correcting the phase shift by frequency f 0 Carrying the interference signal into a 2N frame pure interference image I' (k), performing weighted multi-step phase solving by using a 3-order Blackman squaring window function with the sequence length of 2N, and calculating to obtain an initial phase of the interference signal;
(9) calculating the surface shape distribution of the super surface; calculating to obtain the surface shape distribution of the super surface according to the linear relation between the initial phase of the interference signal and the height of the measured shape obtained by the previous step;
preferably, in the formulation and implementation of the interferogram acquisition scheme, the number of frames acquired for the interferogram after each phase shift is 5 in the interferogram acquisition process, and the weighted average processing is performed, and the specific implementation method is as follows: processing the interferograms with similar theoretical phase shift values of 5 times acquired after phase shift by using a weighted average method with corresponding weights of 0.1, 0.3 and 0.1 to finally obtain processed interferogram light intensity data which is recorded as I (k) and used as light intensity data of the phase shift interferogram of the kth time, wherein the data is specifically expressed as follows: i (k) ═ 0.1 × I 1 (k)+0.3×I 2 (k)+0.3×I 3 (k)+0.3×I 4 (k)+0.1×I 5 (k)]/(0.1+0.3+0.3+0.3+0.1). Recording 5 frames of interferograms acquired after the kth phase shift as I r (k)，r＝1,2,3,4,5。
Preferably, in setting the analysis code of the effective measurement area and solving the background value, when the effective area and the ineffective area of the analysis code are divided, there are two ways corresponding to the circular measurement area and the rectangular measurement area, respectively. Wherein the mask for the circular measurement area is designed, the values within the analysis code matrix follow the following law.
Recording the analysis circle center of the required circular analysis code, namely the image center point as (X) 0 ,Y 0 ) Recording the radius of the analysis circle of the required circular analysis code as R, and having the following rule:
when the point (X, y) on the interferogram satisfies (X-X) 0 ) 2 +(y-Y 0 ) 2 ＜R 2 Then, the value at the midpoint (X, y) of the circular analysis code is set to 1, wherein 0 is more than or equal to X and more than or equal to X T ，0≥y≥Y T And x and y are integers. When the above condition is not satisfied, the value at the point (x, y) in the circular analysis code is set to 0. After the operation of setting 0 and setting 1 for the analysis code element is completed, the condition (X-X) is satisfied 0 ) 2 +(y-Y 0 ) 2 ＝R 2 Satisfy (X-X) 0 ) 2 +(y-Y 0 ) 2 ＝(R+1) 2 Satisfy (X-X) 0 ) 2 +(y-Y 0 ) 2 ＝(R+2) 2 Points in the temporal circular analysis code are recorded as detected edge points, which serve as edge boundaries of the analysis code. When R is set, R is less than or equal to min (X) T ，Y T ) And min is an operation symbol for solving the minimum value of the two numerical values. In the pair X 0 And Y 0 When setting, X is satisfied 0 -3≥R，X 0 +2+R≤X T ，Y 0 -3≥R，Y 0 +2+R≤Y T 。
Preferably, when calculating the respective weighted mean of the respective characteristic signal sequences, the operation can be expressed as
Wherein I U ' (k) means the weighted mean of the characteristic signals in the k frame pure interference pattern obtained by solving, and X (i) is a weight sequence
The elements (A) and (B) in (B),
and Σ is the sum operator. Then calculating characteristic signals in each sequence
Weighted mean value I corresponding thereto U '(k) cross correlation coefficient H' k (i) And constructing the cross-correlation coefficient sequence by using the cross-correlation coefficient sequence as a sequence element
Wherein
Where Cov denotes covariance and Var denotes variance.
Preferably, the sequence is averaged over each interferogram
In the process of expanding Fourier transform, in order to increase interpolation points of a frequency domain in the Fourier transform, increase the resolution of an acquired frequency spectrum, reduce solving errors and perform zero filling operation on a data sequence, wherein the number of zero filling is 6N.
Solving the dephasing correction frequency f by means of Fourier transformation 0 And then, utilizing three frequency values in the frequency spectrum distribution, namely the frequency corresponding to the highest amplitude and two frequencies corresponding to adjacent frequency points. Averaging two frequencies corresponding to adjacent frequency points, and averaging the average value with the frequency corresponding to the highest amplitude value to reduce the error and obtain accurate phase shift correction frequency f 0 。
Preferably, in the step of solving the initial phase of the signal by using the window function and the phase shift correction frequency, in order to further improve the solving precision of the initial phase, a 3-order Blackman squaring window with the length of 2N is used as the window function used by the method, and the performance of the window function is better than that of the Blackman window function.
Compared with the prior art, the invention has the following obvious and prominent substantive characteristics and remarkable advantages:
1. compared with the traditional white light interferometry, the method for measuring the super-surface topography by using the wavelength phase-shifting method provided by the invention has the following obvious advantages: the algorithm is simple, the calculated amount is small, and the solving precision is high;
2. the method for recording the interference pattern by using the multi-frame interference pattern weighted average is characterized in that an effective area and an ineffective area of the interference pattern are divided by using an analysis code, a plurality of sections of integral multiple periods are adopted to collect the interference pattern sequence to carry out time domain light intensity value equalization to remove the influence of background components and background noise in the interference pattern, and a multi-point time domain illumination cross-correlation function-based abnormal data eliminating method is adopted to represent the credible light intensity value by using the multi-point light intensity average value, so that the solving error is greatly reduced, and the method has very important significance for measuring the super surface with high precision;
3. compared with the traditional method, the method for solving the phase shift value based on the time domain discrete Fourier transform greatly improves the solving precision of the phase shift value; the traditional phase shift value solving method comprises the following steps: in the method for changing the phase shift value by wavelength linear tuning, Taylor expansion is carried out on a phase value, a second order and above sub-terms are ignored, a first order term of the phase is used as the phase shift value, phase shift frequency is extracted from the phase shift value, and the interference initial phase is further solved; the method for solving the phase shift value has higher nonlinear error, and is not beneficial to the situation of super surface which needs to obtain high-precision measurement; on the basis of processing the light intensity data of the interference pattern, the method provided by the invention processes the light intensity data points of the phase-shifting interference pattern by using a discrete time domain Fourier transform method, corrects the phase-shifting frequency by using a multi-point frequency value, further increases the solving precision of the phase-shifting value, and establishes a foundation for accurately solving the super-surface shape in the follow-up process;
4. the initial phase of the signal is solved based on the weighted multi-step phase-shifting measurement method and the phase-shifting solution value, and the adopted window function is a Blackman self-multiplying window function of 3 orders, so that the solving precision of the signal frequency is higher than that of the Blackman window function;
5. the method is simple and easy to implement, low in cost and suitable for popularization and application.
Drawings
FIG. 1 is a schematic diagram of a measured super-surface profile structure according to the present invention.
FIG. 2 is a schematic flow chart of the method of the present invention.
FIG. 3 is a schematic diagram of an analysis code matrix according to the present invention.
Detailed Description
The above-described scheme is further illustrated below with reference to specific embodiments, which are detailed below:
the first embodiment is as follows:
in this embodiment, referring to fig. 1, a method for measuring super-surface topography distribution by using a wavelength phase shift method includes the following steps:
(1) acquiring and processing an interference pattern on the super surface by using a wavelength phase-shifting interference technology:
(1-1) phase-shifting acquisition and weighted averaging processing of an interference pattern;
(1-2) screening an effective area by using an interferogram;
(1-3) removing background noise from the interferogram;
(2) correcting the phase shift value based on time domain discrete Fourier transform:
(2-1) extracting characteristic signals of the interferogram;
(2-2) rejecting invalid characteristic signals based on the multipoint time domain illumination cross-correlation coefficient;
and (2-3) solving the phase shift frequency by time domain Fourier transform.
The method for measuring the super-surface topography distribution by using the wavelength phase-shifting method realizes the high-precision measurement of the super-surface, and has the advantages of simple algorithm and small calculated amount.
Example two:
this embodiment is substantially the same as the first embodiment, and is characterized in that:
referring to fig. 2, in this embodiment, in step (1-1), a wavelength tuning phase-shifting interference technique is used to perform interferogram acquisition on the super-surface with the nanorod structure, where the phase-shifting number of interferograms is 2N +3, N is an integer or a non-integer with a fractional part of 0.5, and the total acquisition frame number is 5 × (2N +3), that is, the acquisition frame number of interferograms after each phase shifting is 5; carrying out weighted average processing on the 5 frames of interferograms after each phase shifting, and taking the processed interferograms as the interferograms after the phase shifting, thereby obtaining the total frame number of the interferograms as 2N + 3;
wherein 5 frames of interference patterns with similar theoretical phase shift values acquired after the kth phase shift are marked as I r (k) R is 1, 2, 3, 4, 5, and the corresponding weights are 0.1, 0.3, and 0.1, respectively; and finally obtaining processed data as light intensity data of the kth phase-shifting interference pattern, and recording the data as I (k), wherein the data is specifically expressed as: i (k) ═ 0.1 × I 1 (k)+0.3×I 2 (k)+0.3×I 3 (k)+0.3×I 4 (k)+0.1×I 5 (k)]/(0.1+0.3+0.3+0.3+0.1)；
In the step (1-2), setting the size of the analysis code matrix to be equal to that of the interference pattern, and setting the internal value of the analysis code matrix to be 1 or 0; performing dot multiplication operation on the interference pattern and the analysis code so as to realize screening of an effective area of the interference pattern; setting the effective area of the analysis code to be circular, wherein the numerical values in the matrix of the effective area follow the following rules:
the center of the analysis circle of the required circular analysis code is recorded, namely the center point of the image is (X) 0 ，Y 0 ) Recording the radius of the analysis circle of the required circular analysis code as R, and having the following rule:
when the point (X, y) on the interference pattern is 0 ≧ X ≧ X T ，0≥y≥Y T X and y are integers satisfying (X-X) 0 ) 2 +(y-Y 0 ) 2 ＜R 2 If so, setting the numerical value of the midpoint (x, y) of the circular analysis code to be 1; when the condition is not met, setting the numerical value of the midpoint (x, y) of the circular analysis code to be 0; after the operations of setting 0 and setting 1 are completed, the condition of (X-X) will be satisfied 0 ) 2 +(y-Y 0 ) 2 ＝R 2 Satisfy (X-X) 0 ) 2 +(y-Y 0 ) 2 ＝(R+1) 2 Satisfy (X-X) 0 ) 2 +(y-Y 0 ) 2 ＝(R+2) 2 Taking a point in the circular analysis code as a detection edge point for recording, wherein the detection edge point is taken as an edge boundary of the analysis code; when R is set, R is less than or equal to min (X) T ，Y T ) Min is an operation symbol for solving the minimum value of the two numerical values; in the pair X 0 And Y 0 When setting, X is satisfied 0 -3≥R，X 0 +2+R≤X T ，Y 0 -3≥R，Y 0 +2+R≤Y T 。
In the step (1-3), segmenting the 2N +3 frames of the interferogram, taking the 1 st frame to the 2N frame as a first segment, sequentially staggering the initial frame numbers of the 3 segments of the interferogram to 1, wherein the total frame numbers of the segments are 2N frames; averaging each segment of the interference pattern to obtain a background value of each segment of the interference pattern, and averaging the background values obtained by each segment, wherein the background values can be regarded as the background values of the collected interference pattern, including background components and background noise; and subtracting the background value from the first section of the interference image processed by the analysis code to obtain an approximate pure interference image I' (k), wherein the value range of the k is 1-2N.
In the step (2-1), 2N frames of processed pure interferograms are adopted, and the central point (X) of the image is used in each frame of the interferograms 0 ，Y 0 ) Extracting light intensity data of 9 adjacent positions of the point in the effective region as a geometric center; 2N light intensity data sequences can be constructed by arranging and counting the extraction points of each frame of interferogram from left to right and then from top to bottom, and are represented as
Is recorded as the ith element I 'in the characteristic signal sequence and the kth light intensity data sequence' k (i) Representing the i-th characteristic signal extracted from the k-th frame of clean interferogram.
In the step (2-2), calculating the weighted average value of each characteristic signal sequence as I U ' (k) and calculating the characteristic signal I ' in each sequence ' k (i) Weighted mean value I corresponding thereto U 'the correlation coefficient sequence of (k) is H' k (i) (ii) a And to cross correlation coefficient sequence H' k (i) Arranging descending order in the sequence from big to small, selecting the maximum value and the minimum value, removing the characteristic signals corresponding to the two values, thus remaining 7 characteristic signals in each characteristic signal sequence, and then carrying out equalization processing on each characteristic signal sequence after data removal to obtain 2N light intensity data, which are marked as I' aver (k) And obtaining each as an elementEqualized sequence of interferograms
In the step (2-3), the sequence is equalized for each interferogram
Carrying out extended Fourier transform; will be provided with
Combining with sequence vector composed of zero values with length of 6N to form sequence to be analyzed
Wherein m is 1-8N,
the sequence length of (a) is 6N, all internal elements are 0, and q is an integer distributed in 1-6N. To pair
Performing discrete Fourier transform to obtain frequency spectrum distribution formed by the frequency and the amplitude; in the obtained frequency spectrum distribution, arranging the amplitudes corresponding to the frequencies in a descending order, selecting the frequency corresponding to the maximum amplitude value, and recording as a rough phase-shifting frequency; solving a frequency mean value of 2 frequency points adjacent to the roughly selected phase-shifting frequency in a frequency spectrum, dividing the sum of the values of the 2 frequency points by 2, and recording the obtained result as the roughly corrected phase-shifting frequency; 2 frequency points corresponding to the rough phase shift and the rough frequency correction peak are solved for a frequency mean value, the sum of the values of the 2 frequency points is divided by 2, and the obtained result is recorded as the phase shift correction frequency f 0 。
The method for measuring the super-surface topography by using the wavelength phase-shifting method has the obvious advantages compared with the traditional white light interferometry: the algorithm is simple, the calculated amount is small, and the solving precision is high; in the embodiment, an interferogram is recorded by using a multi-frame interferogram weighted average method, an effective area and an ineffective area of the interferogram are divided by using analysis codes, the influence of background components and background noise in the interferogram is removed by averaging time domain light intensity values in a multi-segment integral-multiple-period acquisition interferogram sequence, and the solving error is greatly reduced by using a multipoint light intensity mean value to represent a credible light intensity value through an abnormal data eliminating method based on a multipoint time domain illumination cross-correlation function.
Example three:
this embodiment is substantially the same as the above embodiment, and is characterized in that:
in the step (1-1), a wavelength tuning phase-shifting interference technology is used for acquiring an interferogram of the super surface with the nano-pillar structure, the phase-shifting frequency of the interferogram is 2N +3, and the total acquisition frame number is 5 x (2N +3), namely the acquisition frame number of the interferogram after each phase shifting is 5, and N is an integer or a non-integer with a decimal part of 0.5; carrying out weighted average processing on the 5 frames of interferograms after each phase shifting, and taking the processed interferograms as the interferograms after the phase shifting, thereby obtaining the total frame number of the interferograms as 2N + 3;
wherein 5 frames of interference patterns with similar theoretical phase shift values acquired after the kth phase shift are marked as I r (k) R is 1, 2, 3, 4, 5, and the corresponding weights are 0.1, 0.3, and 0.1, respectively; and finally obtaining data after weighted averaging as light intensity data of the kth phase-shifting interference pattern, wherein the data is marked as I (k), and the data is specifically represented as: i (k) ═ 0.1 × I 1 (k)+0.3×I 2 (k)+0.3×I 3 (k)+0.3×I 4 (k)+0.1×I 5 (k)]/(0.1+0.3+0.3+0.3+0.1)；
In the step (1-2), setting the size of the analysis code matrix to be equal to that of the interference pattern, and setting the internal value of the analysis code matrix to be 1 or 0; performing dot multiplication operation on the interference pattern and the analysis code so as to realize screening of an effective area of the interference pattern; setting the effective area of the analysis code to be circular, as shown in the third figure, the numerical values in the matrix of the analysis code follow the following rules:
recording the analysis circle center of the required circular analysis code, namely the image center point as (X) 0 ，Y 0 ) Recording the radius of the analysis circle of the required circular analysis code as R, and having the following rule:
when the point (X, y) on the interferogram satisfies (X-X) 0 ) 2 +(y-Y 0 ) 2 ＜R 2 Then, the value of the point (x, y) in the circular analysis code is set to 1. When the condition is not met, the numerical value of the midpoint (X, y) of the circular analysis code is set to be 0, and X is more than or equal to 0 and more than or equal to X T ，0≥y≥Y T X and y are integers; after the operations of setting 0 and setting 1 are completed, the condition of (X-X) will be satisfied 0 ) 2 +(y-Y 0 ) 2 ＝R 2 Satisfy (X-X) 0 ) 2 +(y-Y 0 ) 2 ＝(R+1) 2 Satisfy (X-X) 0 ) 2 +(y-Y 0 ) 2 ＝(R+2) 2 Taking a point in the circular analysis code as a detection edge point for recording, wherein the detection edge point is taken as an edge boundary of the analysis code; when R is set, R is less than or equal to min (X) T ，Y T ) Min is an operation symbol for solving the minimum value of the two numerical values; in the pair X 0 And Y 0 When setting, X is satisfied 0 -3≥R，X 0 +2+R≤X T ，Y 0 -3≥R，Y 0 +2+R≤Y T ；
In the step (1-3), 2N +3 frames of the interferogram are segmented, the 1 st frame to the 2N frame are taken as the first segment, the initial frame numbers of the 3 segments of the interferogram are sequentially staggered to be 1, and the total frame number of the segments is 2N frames. Averaging each segment of the interference pattern to obtain a background value of each segment of the interference pattern, and averaging the background values obtained by each segment, wherein the background values can be regarded as the background values of the collected interference pattern, including background components and background noise; subtracting the background value from the first section of interference image processed by the analysis code to obtain an approximate pure interference image I' (k), wherein the value range of the k is 1-2N;
in the step (2-1), 2N frames of pure interferograms processed by the first embodiment are adopted, and the central point (X) of the image is used in each frame of interferogram 0 ，Y 0 ) Extracting light intensity data of 9 adjacent positions of the point in the effective area as a geometric center; 2N light intensity data sequences can be constructed by arranging and counting the extraction points of each frame of interferogram from left to right and then from top to bottom, and are represented as
Is recorded as the ith element I 'in the characteristic signal sequence and the kth light intensity data sequence' k (i) Representing the ith characteristic signal extracted from the k frame of clean interferogram;
in the step (2-2), calculating the weighted average value of each characteristic signal sequence as I U ' (k) and calculating the characteristic signal I ' in each sequence ' k (i) Weighted mean value I corresponding thereto U 'the correlation coefficient sequence of (k) is H' k (i) (ii) a And for the cross correlation coefficient sequence
Performing descending (from big to small) arrangement in the sequence, selecting the maximum value and the minimum value, and eliminating the characteristic signals corresponding to the two values, so that 7 characteristic signals remain in each characteristic signal sequence, and then performing equalization processing on each characteristic signal sequence after data elimination to obtain 2N light intensity data, which are marked as I' aver (k) And using the interference pattern as an element to obtain an equalization sequence of each interference pattern
In the step (2-3), averaging sequences are applied to the respective interferograms
And carrying out expanded Fourier transform. Will be provided with
Combining with a sequence (vector) composed of zero values with the length of 6N to form a sequence to be analyzed
Wherein m is 1-8N,
the sequence length of (a) is 6N, all internal elements are 0, and q is an integer distributed in 1-6N. For is to
And performing discrete Fourier transform to obtain the frequency spectrum distribution formed by the frequency and the amplitude. In the obtained frequency spectrum distribution, the amplitudes corresponding to the frequencies are arranged in a descending order, and the frequency corresponding to the maximum amplitude value is selected and recorded as the rough selection phase-shifting frequency. The frequency mean (the sum of the values of the 2 frequency points divided by 2) is solved for 2 frequency points adjacent to the coarse shift frequency in the frequency spectrum, and the obtained result is recorded as the coarse shift frequency. Solving the frequency mean value (the sum of the values of the 2 frequency points is divided by 2) of the 2 frequency points corresponding to the rough phase shift and the rough frequency correction peak, and recording the obtained result as the phase shift correction frequency f 0 。
The embodiment uses the wavelength phase shift method to measure the super-surface morphology, and has obvious advantages compared with the traditional white light interferometry: the algorithm is simple, the calculated amount is small, and the solving precision is high; in the embodiment, a multi-frame interferogram weighted average method is used for recording interferograms, analysis codes are used for dividing effective areas and ineffective areas of the interferograms, time domain light intensity values are acquired in an interferogram sequence by adopting a multi-segment integral multiple period to remove influences of background components and background noise in the interferograms in an averaging mode, and solving errors are greatly reduced by using a multipoint light intensity mean value to represent a credible light intensity value through an abnormal data removing method based on a multipoint time domain illumination cross-correlation function.
Example four:
this embodiment is substantially the same as the above embodiment, and is characterized in that:
in this embodiment, a method for solving a surface shape based on a weighted multi-step phase-shift measurement method and a phase-shift solution value includes the following specific contents:
in the invention, the discrete interference light intensity data is weighted by a third-order Blackman window function and the phase value is calculated in multiple steps. Wherein the expression of the third-order Blackman window function is shown in formula (1):
wherein e 0 ＝0.25062,e 1 ＝0.41355,e 2 ＝0.23022,e 3 ＝-0.08405,e 4 ＝0.019032,e 5 ＝-0.0024,e 6 0.000128; k is the total frame number of the interferogram, where K is 2N.
Based on the discrete fourier transform theorem, harmonic signals can be extracted by designing a sampling weight function. The target phase may be demodulated and may be represented in the frequency domain when the sampling weight function is able to effectively act on the corresponding frequency of the target signal and no other signals are introduced. The sampling weight function is shown in equations (2) - (3):
wherein alpha (k) and beta (k) are harmonic sampling coefficients corresponding to interference harmonic signals of the kth interference pattern; b is the light intensity modulation degree;
is the initial phase distribution in the interferogram.
The sampling coefficients α (k) and β (k) corresponding to the harmonics can be obtained by equations (4) to (5):
substituting corresponding harmonic sampling coefficients alpha (k) and beta (k) into the two formulas (2) and (3) respectively, and performing arc tangent on the formulas (2) and (3) to obtain initial wrapping phases of harmonic signals respectively; the recovered initial wrapped phase of the harmonic signal is as shown in equation (6):
after unwrapping, the initial phase distribution of the deskew recoverable harmonic signal is
According to the relationship between the initial phase and the fluctuation of the measured shape, the measured shape can be obtained as shown in formula (7):
wherein λ is 0 Is the initial value of the wavelength.
In summary, in the above embodiment of the present invention, the method for measuring the super-surface topography distribution by using the wavelength phase shift method utilizes the wavelength phase shift interference technique to perform the acquisition processing of the interferogram on the super-surface: phase-shifting acquisition and weighted averaging processing of the interferogram, screening an effective area of the interferogram, and removing background noise from the interferogram. Correcting the phase shift value based on time domain discrete Fourier transform: extracting characteristic signals of the interference pattern, eliminating invalid characteristic signals based on multipoint time domain illumination cross correlation coefficients, and solving phase shift frequency through time domain Fourier transform. The embodiment of the invention has the advantages of simple algorithm, small calculated amount and high solving precision, and has very important significance for high-precision measurement of the super surface.
The embodiments of the present invention have been described with reference to the accompanying drawings, but the present invention is not limited to the embodiments, and various changes and modifications can be made according to the purpose of the invention, and any changes, modifications, substitutions, combinations or simplifications made according to the spirit and principle of the technical solution of the present invention shall be equivalent substitutions, as long as the purpose of the present invention is met, and the present invention shall fall within the protection scope of the present invention without departing from the technical principle and inventive concept of the present invention.
Claims (7)
1. A method for measuring super-surface topography distribution by using a wavelength phase shift method is characterized by comprising the following steps:
(1) acquiring and processing an interference pattern on the super surface by using a wavelength phase-shifting interference technology:
(1-1) phase-shifting acquisition and weighted averaging processing of the interferogram;
(1-2) screening an effective area by using an interferogram;
(1-3) removing background noise from the interferogram;
(2) correcting the phase shift value based on time domain discrete Fourier transform:
(2-1) extracting characteristic signals of the interferogram;
(2-2) eliminating invalid characteristic signals based on the multipoint time domain illumination cross correlation coefficient;
and (2-3) solving the phase shift frequency by time domain Fourier transform.
2. The method for measuring the topographic distribution of a super-surface using a wavelength shift method as set forth in claim 1, wherein: in the step (1-1), a wavelength tuning phase-shifting interference technology method is used for acquiring an interferogram of the super surface with the nano-pillar structure, the phase-shifting times of the interferogram are 2N +3, N is an integer or a non-integer with the decimal part of 0.5, and the total acquisition frame number is 5 x (2N +3), namely the acquisition frame number of the interferogram after each phase shifting is 5; carrying out weighted average processing on the 5 frames of interferograms after each phase shifting, and taking the processed interferograms as the interferograms after the phase shifting, thereby obtaining the total frame number of the interferograms as 2N + 3; wherein 5 frames of interference patterns with similar theoretical phase shift values acquired after the kth phase shift are marked as I r (k) R is 1, 2, 3, 4, 5, and their corresponding weights are 0.1, 0.3, 0.1, respectively; finally, the processed data is obtained and used as the light intensity data of the kth phase-shifting interferogram, and is marked as I (k), and the data is specifically expressed as follows: i (k) ═ 0.1 × I 1 (k)+0.3×I 2 (k)+0.3×I 3 (k)+0.3×I 4 (k)+0.1×I 5 (k)]/(0.1+0.3+0.3+0.3+0.1)。
3. The method for measuring the topographic distribution of a super-surface using a wavelength shift method as set forth in claim 1, wherein: in the step (1-2), setting the size of the analysis code matrix to be equal to that of the interference pattern, and setting the internal value of the analysis code matrix to be 1 or 0; performing dot multiplication operation on the interference pattern and the analysis code so as to realize screening of an effective area of the interference pattern; setting the effective area of the analysis code to be circular, wherein the numerical values in the matrix of the effective area follow the following rules:
recording the analysis circle center of the required circular analysis code, namely the image center point as (X) 0 ，Y 0 ) Recording the radius of the analysis circle of the required circular analysis code as R, and having the following rule:
when the point (X, y) on the interference pattern is 0 ≧ X ≧ X T ，0≥y≥Y T X and y are integers satisfying (X-X) 0 ) 2 +(y-Y 0 ) 2 ＜R 2 If so, setting the numerical value of the midpoint (x, y) of the circular analysis code to be 1; when the condition is not met, setting the numerical value of the midpoint (x, y) of the circular analysis code to be 0; after the operations of setting 0 and setting 1 are completed, the condition of (X-X) will be satisfied 0 ) 2 +(y-Y 0 ) 2 ＝R 2 Satisfy (X-X) 0 ) 2 +(y-Y 0 ) 2 ＝(R+1) 2 Satisfy (X-X) 0 ) 2 +(y-Y 0 ) 2 ＝(R+2) 2 Taking a point in the circular analysis code as a detection edge point for recording, wherein the detection edge point is taken as an edge boundary of the analysis code; when R is set, R is less than or equal to min (X) T ，Y T ) Min is an operation symbol for solving the minimum value of the two numerical values; in the pair X 0 And Y 0 When setting, X is satisfied 0 -3≥R，X 0 +2+R≤X T ，Y 0 -3≥R，Y 0 +2+R≤Y T 。
4. The method for measuring the super-surface topography distribution using the wavelength phase-shifting method according to claim 1, wherein: in the step (1-3), segmenting the 2N +3 frames of the interferogram, taking the 1 st frame to the 2N frame as a first segment, sequentially staggering the initial frame numbers of the 3 segments of the interferogram to 1, wherein the total frame numbers of the segments are 2N frames; averaging each segment of the interference pattern to obtain a background value of each segment of the interference pattern, and averaging the background values obtained by each segment, wherein the background values can be regarded as the background values of the collected interference pattern, including background components and background noise; and subtracting the background value from the first section of interferogram after the analysis code processing to obtain an approximate pure interferogram I' (k), wherein the value range of the k is 1-2N.
5. The method for measuring the super-surface topography distribution using the wavelength phase-shifting method according to claim 1, wherein: in the step (2-1), 2N frames of pure interferograms processed by the first embodiment are adopted, and the central point (X) of the image is used in each frame of interferogram 0 ，Y 0 ) Extracting light intensity data of 9 adjacent positions of the point in the effective area as a geometric center; 2N light intensity data sequences can be constructed by arranging and counting the extraction points of each frame of interferogram from left to right and then from top to bottom, and are represented as
Is recorded as a characteristic signal sequence, and the ith element Γ 'in the kth light intensity data sequence' k (i) Representing the i-th characteristic signal extracted from the k-th frame of clean interferogram.
6. The method for measuring the super-surface topography distribution using the wavelength phase-shifting method according to claim 1, wherein: in the step (2-2), calculating the weighted average value of each characteristic signal sequence as I U ' (k) and calculating the characteristic signal Γ ' in each sequence ' k (i) Weighted mean value I corresponding thereto U 'the correlation coefficient sequence of (k) is H' k (i) (ii) a And to cross correlation coefficient sequence H' k (i) Arranging descending order in the sequence from big to small, selecting the maximum value and the minimum value, removing the characteristic signals corresponding to the two values, thus remaining 7 characteristic signals in each characteristic signal sequence, and then carrying out equalization processing on each characteristic signal sequence after data removal to obtain 2N light intensity data, which are marked as I' aver (k) And using the interference pattern as an element to obtain an equalization sequence of each interference pattern
7. Use of wavelength shifting according to claim 1The method for measuring the super-surface topography distribution by the phase method is characterized by comprising the following steps: in the step (2-3), the sequence is equalized for each interferogram
Carrying out extended Fourier transform; will be provided with
Combining with sequence vector composed of zero values with length of 6N to form sequence to be analyzed
Wherein m is 1-8N,
the sequence length of (a) is 6N, all internal elements are 0, and q is an integer distributed in 1-6N. To pair
Performing discrete Fourier transform to obtain frequency spectrum distribution formed by the frequency and the amplitude; in the obtained frequency spectrum distribution, arranging the amplitudes corresponding to the frequencies in a descending order, selecting the frequency corresponding to the maximum amplitude value, and recording as a rough phase-shifting frequency; solving a frequency mean value of 2 frequency points adjacent to the roughly selected phase-shifting frequency in a frequency spectrum, dividing the sum of the values of the 2 frequency points by 2, and recording the obtained result as the roughly corrected phase-shifting frequency; 2 frequency points corresponding to the rough phase shift and the rough frequency correction peak are solved for a frequency mean value, the sum of the values of the 2 frequency points is divided by 2, and the obtained result is recorded as the phase shift correction frequency f 0 。
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