CN109813233B - Phase subdivision method based on wavelet transformation - Google Patents
Phase subdivision method based on wavelet transformation Download PDFInfo
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- CN109813233B CN109813233B CN201910089381.8A CN201910089381A CN109813233B CN 109813233 B CN109813233 B CN 109813233B CN 201910089381 A CN201910089381 A CN 201910089381A CN 109813233 B CN109813233 B CN 109813233B
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Abstract
The invention discloses a phase subdivision method based on wavelet transformation, which comprises the steps of converting an optical interference signal formed by a moving grating and a fixed grating into an electric signal, and sampling the electric signal to obtain sampling data; performing wavelet transformation on the sampling data to obtain the instantaneous frequency of each sampling point, fitting each section of the sampling point and obtaining a first frequency curve; determining intermediate frequency between two adjacent end points in the first frequency curve, fitting the intermediate frequency point between the two end points to obtain an optimized frequency curve, and distributing sampling points between the two end points according to the fitted frequency curve; carrying out error detection on the optimized frequency curve to obtain the optimized frequency of the sampling point; calculating the instantaneous frequency f (t + delta t) of the time point after the time delta t from the time t, setting the phase obtained after the time interval delta t to be 2 pi/N, and counting N while calculating the time interval delta t; and calculating the movement distance of the movement grating according to the movement relation.
Description
Technical Field
The invention relates to the technical field of signal processing, in particular to a phase subdivision method based on wavelet transformation.
Background
With the rapid development of science and technology, the requirements of various industries on high-precision measurement technology are higher and higher, and especially the requirements on the high-precision measurement technology are higher in the industries related to nanotechnology, MEMS (micro electro mechanical system) technology and aerospace technology.
Since the requirements for signal accuracy are higher, further processing of the measured signals is required for subdivision without any means to improve the accuracy of the measurement instrument. The general subdivision method cannot meet higher requirements due to the limitation of subdivision multiples, overlarge error, complex structure and the like. The electronic subdivision methods used today are roughly divided into two categories, one based on the amplitude of the signal and the other based on the phase of the signal. The subdivision based on the amplitude of the signal is to directly process the signal, the motion is represented by amplitude information, but the resistance to noise interference is weak and is easily influenced by the noise interference, the subdivision based on the phase of the signal has strong resistance to the noise interference, the quality requirement on the signal is lower than that of other methods, and the subdivision accuracy is improved.
In the prior art, phase or frequency information of a signal at each sampling point is obtained through wavelet transformation, then phase differences of adjacent sampling points are obtained, the sum of the phase differences of the adjacent sampling points is the phase change of the period of time, and then the motion change represented by the signal phase change can be obtained. The phase difference of each adjacent sampling point is the subdivided phase, but since the sampling time is determined and the frequency is continuously changed, the phase difference of each adjacent sampling point is also changed, namely the subdivision multiple is continuously changed. The subdivision multiple changes, the subdivision precision of the signal also changes, and the subdivision effect also changes along with the frequency of each point.
Disclosure of Invention
In view of the above, an object of the present invention is to provide a phase subdivision method based on wavelet transformation, which is based on the problem related to high-precision positioning of a lithography machine, wherein a signal to be measured is formed by irradiating laser light onto two gratings, one grating is a moving grating mounted on a moving stage, the other grating is fixed on a fixed stage, the two diffracted lights are adjusted to form interference signals on a detector, and the moving distance of the moving stage is obtained by calculating the movement of interference fringes according to the doppler effect.
The invention solves the technical problems by the following technical means:
a phase subdivision method based on wavelet transformation comprises the following steps:
converting an optical interference signal formed by the moving grating and the fixed grating into an electric signal, and sampling the electric signal to obtain sampling data;
performing wavelet transformation on the sampling data to obtain the instantaneous frequency of each sampling point, fitting each section of the sampling point and obtaining a first frequency curve;
determining intermediate frequency between two adjacent end points in the first frequency curve, fitting the intermediate frequency point between the two end points to obtain an optimized frequency curve, and distributing sampling points between the two end points according to the fitted frequency curve;
carrying out error detection on the optimized frequency curve, and carrying out error compensation to obtain the optimized frequency of the sampling point;
calculating the elapsed time delta from time ttThen, the instantaneous frequency f (t + Δ) at the time pointt) Let us set the elapsed time interval ΔtThe phase obtained is 2 pi/n, the time interval delta is calculatedtWhile counting N, each time Δ is calculatedtRepresenting the phase of the signal over 2 pi/n, calculating said time interval deltatWhen setting said time interval ΔtThe frequency of the signal in the frequency-invariant phase-invariant time T is 1/(n f (i)) with the phase change of 2 pi/n, wherein n is a subdivision multiple, f (i) is the current frequency, the frequency f (j) of the elapsed time T is obtained, the change function of the frequency is further obtained, and the time delta of the phase change of 2 pi/n is obtained according to the change function of the frequencyt；
And calculating the movement distance of the movement grating according to the movement relation.
Furthermore, the moving grating is installed on a moving platform, and the moving distance of the moving grating is the moving distance of the moving platform.
Further, the sampling the electrical signal to obtain sampling data includes:
and performing telescopic translation by taking the Morlet function as a basic function to obtain a series of wavelet sequences, performing wavelet transformation on the electric signals, and finally extracting the modulus maximum of the electric signals to obtain the instantaneous frequency of the signals.
And further optimizing the frequency of the inflection point, wherein the method for optimizing the frequency of the inflection point comprises the step of dividing the inflection point into two front and rear half parts for processing respectively, wherein the front half part is calculated by a front sampling point, and the rear half part is calculated by a rear sampling point.
And further, optimizing the signal frequencies at the two ends, wherein the method for optimizing the signal frequencies at the two ends comprises the steps of discarding the data of the front end point and the rear end point and extending the data by the frequency and frequency difference of adjacent sampling points.
The invention has the beneficial effects that: the invention is based on the subdivision of the phase of the signal, so the anti-interference ability to the noise is stronger compared with the common method based on the subdivision of the amplitude, and meanwhile, compared with other methods based on the subdivision of the phase, the invention has some progress, so that the subdivision multiple is more stable, simultaneously, the frequency of the subdivided signal is improved, the sampling frequency is reduced, and the pressure of the sampling element is relieved.
Drawings
FIG. 1 is a flow chart of a phase subdivision method based on wavelet transform of the present invention;
FIG. 2 is a graph of wavelet coefficient modulus values as a function of scale factor a for determination of a shift factor b provided by an embodiment of the present invention;
FIG. 3 is a graph of the frequency variation of an unoptimized signal provided by an embodiment of the present invention;
FIG. 4 is a graph of a partial amplification of the frequency change of an unoptimized signal provided by an embodiment of the present invention;
fig. 5 is a graph of frequency variation of an optimized signal provided by an embodiment of the present invention.
Detailed Description
The invention will be described in detail below with reference to the following figures and specific examples:
as shown in fig. 1, a phase subdivision method based on wavelet transform of the present invention includes:
converting an optical interference signal formed by the moving grating and the fixed grating into an electric signal, and sampling the electric signal to obtain sampling data;
performing wavelet transformation on the sampling data to obtain the instantaneous frequency of each sampling point, fitting each section of the sampling point and obtaining a first frequency curve;
determining intermediate frequency between two adjacent end points in the first frequency curve, fitting the intermediate frequency point between the two end points to obtain an optimized frequency curve, and distributing sampling points between the two end points according to the fitted frequency curve;
carrying out error detection on the optimized frequency curve, and carrying out error compensation to obtain the optimized frequency of the sampling point;
calculating the elapsed time delta from time ttThen, the instantaneous frequency f (t + Δ) at the time pointt) Let us set the elapsed time interval ΔtThe phase obtained is 2 pi/n, the time interval delta is calculatedtWhile counting N, each time Δ is calculatedtIndicating that the phase of the signal has passed 2 pi/n;
and calculating the movement distance of the movement grating according to the movement relation.
Specifically, the moving grating is mounted on a moving platform, and the moving distance of the moving grating is the moving distance of the moving platform.
Optionally, the sampling the electrical signal to obtain sampling data includes:
and performing telescopic translation by taking the Morlet function as a basic function to obtain a series of wavelet sequences, performing wavelet transformation on the electric signals, and finally extracting the modulus maximum of the electric signals to obtain the instantaneous frequency of the signals.
Specifically, a scale factor a and a translation factor b are used when obtaining the wavelet sequence, where the scale factor a represents the width, i.e., frequency, of the warped basis function, and the translation factor b represents the position of the translated basis function. When the frequency of the signal is around the frequency represented by the scale factor a, as shown in fig. 2, the frequency in both black lines is displayed as the frequency represented by the scale factor a. When the sampling frequency is too fast or the frequency of the signal changes slowly, a phenomenon as shown in fig. 3 is obtained, and the frequencies of many sampling points are equal in a phase manner.
Specifically, it can be roughly determined by analysis that the frequencies of some points are adjacent sampling points as shown in fig. 4, and the frequencies of two points are very close, because the point a is closer to F1 and the point B is closer to F, so it can be determined that the frequency of one point between the point a and the point B is the middle value of F1 and F, assuming that this point is the middle point E between a and B, and similarly F is the middle point of C and D.
After the frequencies of the front end point and the rear end point are respectively determined as (f1+ f)/2 and (f + f2)/2, the number x of sampling points with equal frequencies is known in a counting mode, the frequency of the signal is set to change in a straight line function, the change function of the signal is fitted to be (f1+ f)/2+ c (f2-f1)/(2 x), wherein c represents the position of the sampling points, and the optimized signal is shown in fig. 5.
Further, the method further comprises optimizing the frequency of the inflection point, wherein the frequency change of the signal at the inflection point changes between increase and decrease, namely the product of the frequency difference of the front step and the frequency difference of the rear step is less than 0, so that the signal needs to be processed separately.
Further, the method also comprises the step of optimizing the frequencies of the signals at the two ends, and because the frequencies obtained by processing the signals are related front and back, the signals at the two ends lack related signals front and back, so that the signals after being processed have large fluctuation and cannot be directly used, and the optimization is needed. The method for optimizing the signal frequencies at the two ends comprises the steps of discarding the data of the front end point and the rear end point and extending the data by the frequency and frequency difference of adjacent sampling points. In this embodiment, after the optimization of the inflection point, the port, and the signal itself is completed, error detection is performed, and a certain error compensation is performed, and after the error compensation is performed, the average value of the frequency errors of the obtained sampling points is-0.0019, which is greatly improved compared with 0.3415 when the optimization is not performed.
Further, the time interval Δ is calculatedtWhen setting said time interval ΔtThe time required for the phase change of 2 pi/n when the frequency of the internal signal is unchanged is T, and the time T which is constantly changed and is obtained by the frequency is required to be actually processed. Then, the frequency of the point after the time T is obtained, and the time interval Delta is calculated according to the frequencytThe frequency of the next point is calculated. If the frequency f (i) is assumed to be constant in a short time, the subdivision multiple is n, and the time period T required to elapse is 1/(n × f (i)).
In particular, at a calculation time interval ΔtThe frequency is assumed to be constant, but in practice the frequency is changing, so the time interval Δ is determinedtThere is also a certain error. To solve this problem, it is still assumed that the frequency is constant as f (i), and the subdivision multiple is n, so that the time interval T is 1/(n × f (i)), and the frequency obtained over the time T is f (j). In this case, it is assumed that the frequency changes uniformly within the time T, the rate of change of the frequency is (f (j) -f (i))/T, the formula of the change of the frequency within the time T is f (T) ((i)) + T (f (j) -f (i))/T, and the phase obtained after the elapse of the time T is 2 pi/n, that is, the formula of the frequency is from 0 to Δ ═ f (i))/TtIs integrated by 2 pi/n in between A>Time interval delta is obtained at 0t(2/(n x A) + (f (i))/A) ^2) ^0.5-f (i))/A at<When 0, the time is- (2/(n × A) + (f (i)/A) ^2) ^0.5-f (i)/A. At the calculated time deltatWhen N is counted, each time N is counted, the phase of the signal passes 2 pi/N, and then the moving distance of the moving platform can be calculated according to the correlation between the phase and the moving.
The phase of the subdivision calculated by the scheme is compared with the phase of the subdivision desired to be achieved, wherein the subdivision multiple n is 1024, the sampling frequency is 10kHz, and the obtained results are shown in table 1.
TABLE 1 Difference between subdivided phases of the scheme and subdivided phases of 1024 subdivision multiples
The frequency data of the obtained signal is optimized, and the frequency represented by the scale factor a in the wavelet transformation is the brought error, so that the data is processed after being obtained, the error between the data and the real data is reduced as much as possible, and the influence on the following scheme is reduced. Then, the time of motion after subdivision is calculated by the frequency data of the obtained signal, the frequency of the signal is considered to be fixed in a short time, the time of motion required for reaching the corresponding subdivision multiple can be obtained according to the formula T1/(n f (i)), wherein n is the subdivision multiple, f (i) is the frequency at the time, after the time of motion T is obtained, the frequency f (j) can be obtained according to the calculation, the frequency is considered to be changed at a constant speed in the period of time, so that the change rate of the frequency in the period of time can be obtained, further the motion time for reaching the corresponding subdivision multiple by the change of the frequency under the condition of the change rate, the change of the phase of the signal in the obtained motion time can be kept at the required subdivision phase, and the motion time has the capability of stabilizing the subdivision multiple without great fluctuation, accordingly, the requirements of subdividing higher frequency signals and reducing sampling frequency equipment can be met under the condition of stabilizing the subdivision multiple.
Although the present invention has been described in detail with reference to the preferred embodiments, it will be understood by those skilled in the art that various changes may be made and equivalents may be substituted without departing from the spirit and scope of the invention as defined in the appended claims. The techniques, shapes, and configurations not described in detail in the present invention are all known techniques.
Claims (5)
1. A phase subdivision method based on wavelet transform, characterized by comprising:
converting an optical interference signal formed by the moving grating and the fixed grating into an electric signal, and sampling the electric signal to obtain sampling data;
performing wavelet transformation on the sampling data to obtain the instantaneous frequency of each sampling point, fitting each section of the sampling point and obtaining a first frequency curve;
determining intermediate frequency between two adjacent end points in the first frequency curve, fitting the intermediate frequency point between the two end points to obtain an optimized frequency curve, and distributing sampling points between the two end points according to the fitted frequency curve;
carrying out error detection on the optimized frequency curve, and carrying out error compensation to obtain the optimized frequency of the sampling point;
calculating the elapsed time delta from time ttThen, the instantaneous frequency f (t + Δ) at the time pointt) Setting elapsed timeInterval deltatThe phase obtained is 2 pi/n, the time interval delta is calculatedtWhile counting N, each time Δ is calculatedtRepresenting the phase of the signal over 2 pi/n, calculating said time interval deltatWhen setting said time interval ΔtThe frequency of the signal in the frequency-invariant phase-invariant time T is 1/(n f (i)) with the phase change of 2 pi/n, wherein n is a subdivision multiple, f (i) is the current frequency, the frequency f (j) of the elapsed time T is obtained, the change function of the frequency is further obtained, and the time delta of the phase change of 2 pi/n is obtained according to the change function of the frequencyt；
And calculating the movement distance of the movement grating according to the movement relation.
2. The phase subdivision method based on wavelet transformation as recited in claim 1, wherein said motion grating is mounted on a motion stage, and the distance of motion of said motion grating is the distance of motion of said motion stage.
3. The wavelet transform-based phase subdivision method of claim 2, wherein the sampling the electrical signal to obtain sampled data comprises:
and performing telescopic translation by taking the Morlet function as a basic function to obtain a series of wavelet sequences, performing wavelet transformation on the electric signals, and finally extracting the modulus maximum of the electric signals to obtain the instantaneous frequency of the signals.
4. The phase subdivision method based on wavelet transformation as recited in claim 3, further comprising optimizing the frequency of the inflection point of the frequency variation, wherein the method for optimizing the frequency of the inflection point comprises dividing the inflection point into two front and rear halves, respectively, and processing the front half and the rear half, respectively, the front half being calculated by the front sampling point and the rear half being calculated by the rear sampling point.
5. The wavelet transform-based phase subdivision method of claim 4, further comprising optimizing the signal frequencies at both ends by discarding the data at the front end point and the back end point and extending the frequency and frequency difference of adjacent sampling points.
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