CN109813233A - A kind of phase subdivision method based on wavelet transformation - Google Patents
A kind of phase subdivision method based on wavelet transformation Download PDFInfo
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Abstract
The phase subdivision method based on wavelet transformation that the invention discloses a kind of including the optical interference signal of moving grating and fixed grating formation is converted into electric signal, and samples the electric signal, obtains sampled data；Sampled data progress wavelet transformation is obtained into the instantaneous frequency of each sampled point, each section of sampled point is fitted and obtains first frequency curve；It determines the intermediate frequency in first frequency curve between adjacent both ends point, and is fitted the intermediate frequency point between each two-end-point to obtain optimization frequency curve, the sampled point between two-end-point is distributed according to the frequency curve of fitting；Error-detecting is carried out to optimization frequency curve, obtains the optimization frequency of sampled point；After calculating begins to pass through time Δ t from time t, (t+ Δ t) carries out counting N while calculating time interval Δ t if the phase obtained after time interval Δ t is 2 π/n to the instantaneous frequency f at place time point；The distance of the moving grating movement is calculated according to movement relation.
Description
Technical field
The present invention relates to signal processing technology field more particularly to a kind of phase subdivision methods based on wavelet transformation.
Background technique
With the fast development of science and technology, requirement of the every profession and trade to Technology Precision is higher and higher, especially relates to
And arrive nanotechnology, the industry of MEMS (MEMS) technology and aeronautical and space technology, the requirement to Technology Precision
It is just higher.
Since the requirement to signal accuracy is higher, in the case where having no idea to improve the precision of measuring instrument, just need
Further processing is carried out to the signal measured to be finely divided.General divided method is due to subdivision multiple limitation, error
The excessive and reasons such as structure is complicated can no longer meet higher requirement.And the electronic fine-grained method used now is roughly divided into
Two kinds, one is amplitudes signal-based to be finely divided, and the phase that another kind is namely based on signal is finely divided.It is signal-based
Amplitude, which is finely divided, is exactly directly handled signal, and movement is represented by amplitude information, but for the resistance energy of noise jamming
Power is weaker, is easy to be influenced by noise jamming, phase signal-based is finely divided the resistivity for noise jamming
It is relatively strong, the quality requirement of signal is compared with other methods and wants low, the accuracy of subdivision also just increases.
Existing technology is that signal is obtained by wavelet transformation in the phase or frequency information of each sampled point, is then acquired
The phase difference of neighbouring sample point, the phase difference of each neighbouring sample point and be exactly the phase change of this period, and then can obtain
The motion change representative to signal phase variation.And the difference of the phase of each neighbouring sample point is exactly the phase segmented, but
Due to the sampling time be it is determining, frequency is continually changing, so the difference of the phase of each neighbouring sample point is also to become
Change, that is, the multiple segmented is constantly changing.Changing occurs in subdivision multiple, and also becomes to the precision of the subdivision of signal
Change, subdivision effect also will appear quality as the frequency of each point changes.
Summary of the invention
In view of this, the object of the present invention is to provide a kind of phase subdivision method based on wavelet transformation, is based on litho machine
High accuracy positioning correlation project and come, the signal for needing to measure is by forming diffraction light in laser irradiation to two gratings one
A grating is that moving grating is mounted on sports platform, another grating is fixed on fixed station, and two beam diffraction lights are adjusted
Interference signal is formed on detector, according to Doppler effect obtained by calculating the movement of interference fringe the movement of sports platform away from
From.
The present invention solves above-mentioned technical problem by following technological means:
A kind of phase subdivision method based on wavelet transformation, comprising:
The optical interference signal that moving grating and fixed grating are formed is converted into electric signal, and the electric signal is carried out
Sampling, obtains sampled data；
Sampled data progress wavelet transformation is obtained into the instantaneous frequency of each sampled point, each section of sampled point is fitted
And obtain first frequency curve；
Determine the intermediate frequency in first frequency curve between adjacent both ends point, and by the intermediate frequency between each two-end-point
Point is fitted to obtain optimization frequency curve, and the sampled point between two-end-point is distributed according to the frequency curve of fitting；
Error-detecting is carried out to optimization frequency curve, and carries out error compensation, obtains the optimization frequency of sampled point；
After calculating begins to pass through time Δ t from time t, instantaneous frequency f (the t+ Δ t), if pass through at place time point
Between the phase that obtains after interval of delta t be 2 π/n, carry out counting N while calculating time interval Δ t, it is every to calculate a Δ t and indicate
The phase of signal have passed through 2 π/n；
The distance of the moving grating movement is calculated according to movement relation.
Further, the moving grating is mounted on a sports platform, and the distance of the moving grating movement is the movement
The distance of platform movement.
Further, described that the electric signal is sampled, obtain sampled data, comprising:
Carry out the electric signal after flexible translation obtains a series of wavelet sequences using morlet function as basic function
Wavelet transformation extracts the modulus maximum of the electric signal finally to obtain the instantaneous frequency of signal.
It further, further include being optimized to the frequency of inflection point, the method that the frequency to inflection point optimizes includes
Inflection point punishment is respectively processed at two two half parts of front and back, first half is calculated by preceding sampled point, and rear part is by rear
Sampled point is calculated.
It further, further include being optimized to the signal frequency at both ends, what the signal frequency to both ends optimized
Method is to be extended the rejection of data of forward terminal, aft terminal by the frequency and difference on the frequency of neighbouring sample point.
Further, when calculating the time interval Δ t, the signal frequency set in the time interval Δ t is constant, obtains
2 π of phase change/n time T=1/ (n*f (i)), wherein n is the multiple of subdivision, and f (i) is current frequency, is obtained by the time
The frequency f (j) of T, and then the variation function of frequency is obtained, function is changed according to frequency and acquires 2 π of phase change/n time Δ t.
Beneficial effects of the present invention: the present invention is the subdivision that phase signal-based carries out, so being based on width with general
The method of value subdivision is based on phase subdivision method with other and compares and have compared to stronger to the anti-interference ability of noise
Progress so that the multiple of subdivision is more stable, while improving the frequency of the signal of subdivision, reduces the frequency of sampling, alleviate
The pressure of sampling element.
Detailed description of the invention
Fig. 1 is a kind of flow chart of the phase subdivision method based on wavelet transformation of the present invention；
Fig. 2 be when shift factor b provided in an embodiment of the present invention is determined wavelet module value with the variation of scale factor a
Curve graph；
The frequency variation curve figure of signal when Fig. 3 is provided in an embodiment of the present invention is not optimised；
The frequency of signal changes partial enlargement curve graph when Fig. 4 is provided in an embodiment of the present invention is not optimised；
Fig. 5 is the frequency variation curve figure of the signal after optimization provided in an embodiment of the present invention.
Specific embodiment
Below with reference to the drawings and specific embodiments, the present invention is described in detail:
As shown in Figure 1, a kind of phase subdivision method based on wavelet transformation of the invention, comprising:
The optical interference signal that moving grating and fixed grating are formed is converted into electric signal, and the electric signal is carried out
Sampling, obtains sampled data；
Sampled data progress wavelet transformation is obtained into the instantaneous frequency of each sampled point, each section of sampled point is fitted
And obtain first frequency curve；
Determine the intermediate frequency in first frequency curve between adjacent both ends point, and by the intermediate frequency between each two-end-point
Point is fitted to obtain optimization frequency curve, and the sampled point between two-end-point is distributed according to the frequency curve of fitting；
Error-detecting is carried out to optimization frequency curve, and carries out error compensation, obtains the optimization frequency of sampled point；
After calculating begins to pass through time Δ t from time t, instantaneous frequency f (the t+ Δ t), if pass through at place time point
Between the phase that obtains after interval of delta t be 2 π/n, carry out counting N while calculating time interval Δ t, it is every to calculate a Δ t and indicate
The phase of signal have passed through 2 π/n；
The distance of the moving grating movement is calculated according to movement relation.
Specifically, the moving grating is mounted on a sports platform, the distance of the moving grating movement is the movement
The distance of platform movement.
Optionally, described that the electric signal is sampled, obtain sampled data, comprising:
Carry out the electric signal after flexible translation obtains a series of wavelet sequences using morlet function as basic function
Wavelet transformation extracts the modulus maximum of the electric signal finally to obtain the instantaneous frequency of signal.
Specifically, using scale factor a and shift factor b when obtaining wavelet sequence, scale factor a is represent through stretching
Width, that is, frequency of basic function after contracting, shift factor b represent the position of the basic function after translating.When the frequency of signal exists
When near frequency representated by scale factor a, as shown in Fig. 2, the frequency among two black lines can all be shown as scale factor a institute
The frequency of representative.When sample frequency is too fast or the variation of the frequency of signal is slower, phenomenon as shown in Figure 3 will be obtained, is had very
The interim equal situation of the frequency of multi-point sampling.
Specifically, frequency such as Fig. 4, A point of some points can substantially be determined by analysis and B point is neighbouring sample point, two
Dot frequency is very close, because A point is closer to f1, B point is closer to f, it is possible to determine the frequency for having any between point A and point B
Rate is the median of f1 and f, it is assumed that this point is A and B intermediate point E, and similarly F is the intermediate point of C and D.
Know after the frequency for determining rear and front end point respectively (f1+f)/2 and (f+f2)/2, then by way of counting
After the number x of the equal sampled point of frequency, the frequency for setting this segment signal is linear function variation, passes through the frequency of two-end-point
It is f (c)=(f1+f)/2+c* (f2-f1)/(2*x) that the number of sampled point, which fits the variation function of this segment signal, between endpoint,
Wherein c indicates the position of sampled point, and the signal after optimization is as shown in Figure 5.
Further, further include being optimized to the frequency of inflection point, indicate that the frequency variation of signal is increasing and dropping at inflection point
It changes between low, i.e. the product of former and later two staircase frequencies difference is less than 0, so needing individually to be handled, specifically, institute
Stating to the method that the frequency of inflection point optimizes includes being respectively processed inflection point punishment at two two half parts of front and back, first half
Divide and calculated by preceding sampled point, rear part is calculated by post-sampling point.
It further, further include being optimized to the signal frequency at both ends, since the frequency handled signal is
There is forward-backward correlation, so having lacked the correlation signal of front and back to the signal at both ends, so will appear after treatment very big
Fluctuation, cannot directly use, so needing to optimize.The method that the signal frequency to both ends optimizes is by front end
The rejection of data of point, aft terminal is extended by the frequency and difference on the frequency of neighbouring sample point.In the present embodiment, turned to signal
After the completion of point, port and signal itself optimize, needs to carry out error-detecting, carry out certain error compensation, missed
Difference compensation after, the mean value of the frequency error of obtained sampled point be -0.0019 than being not optimised when 0.3415 have it is very big
It improves.
Further, when calculating the time interval Δ t, the constant phase of signal frequency in the time interval Δ t is set
The time that position variation 2 π/n need is T, and that when actual treatment needs is exactly continually changing time T, the time T be by
Frequency acquires.Then the frequency put after time T is obtained again, then by this frequency meter evaluation time interval of delta t, seeks next point
Frequency.If it is assumed that frequency f (i) is constant in a short time, the multiple of subdivision is n, obtains needing elapsed time section T=1/
(n*f(i))。
Specifically, think that frequency is constant when calculating time interval Δ t, but in practice frequency be in variation,
In the hope of time interval Δ t also just have certain error.In order to solve this problem, still first think that frequency is constant
It is f (i), subdivision multiple is n, so time interval T=1/ (n*f (i)), and be f (j) by the frequency that time T is obtained.At this time
Assuming that for frequency in even variation, the change rate of frequency is A=(f (j)-f (i))/T, change of the frequency in time T in time T
Change formula is exactly to frequency if the phase obtained after time Δ t is 2 π/n for f (t)=f (i)+t* (f (j)-f (i))/T
Formula is equal to 2 π/n to integral is carried out between Δ t 0, and time interval Δ t=(2/ (n*A)+(f (i)/A) ^2) is obtained in A > 0
^0.5-f (i)/A obtains time=- (2/ (n*A)+(f (i)/A) ^2) ^0.5-f (i)/A in A < 0.Calculating time Δ t's
When carry out counting N, the phase that every calculating once just represents signal have passed through 2 π/n, then further according to phase with the phase of movement
Pass relationship can calculate the distance of sports platform movement.
The phase for the subdivision being calculated by this programme and wish that the phase of the subdivision reached compares, wherein segmenting
Multiple n=1024, sample frequency 10kHz, obtain that the results are shown in Table 1.
The difference of the phase of 1 scheme of table subdivision and the subdivision phase of 1024 subdivision multiples
The present invention optimizes processing by the frequency data to obtained signal, by wavelet transformation mesoscale factor a institute
The frequency of representative is exactly bring error, so being handled again after obtaining data, so that the mistake of data and truthful data
Difference is small as far as possible, reduces the influence to scheme below.Then it is transported after elaborate division by calculation by the frequency data of obtained signal
The dynamic time, first think signal frequency be in a short time it is fixed, can be wanted according to formula T=1/ (n*f (i))
Reach the time that corresponding subdivision multiple needs to move, wherein n is the multiple of subdivision, and f (i) is frequency at this time, is being transported
After dynamic time T, frequency f (j) can be obtained according to operation, it is believed that frequency at the uniform velocity changes during this period, so just
Can obtain the change rate of frequency during this period, so available frequency in the hope of change rate variation in the case where want
Reach the run duration that corresponding subdivision multiple is, the variation of the phase of signal can be maintained at and want in the run duration that this is acquired
The subdivision phase asked, does not have very big fluctuation, so possessing the ability of Subdivision multiple, can stablize carefully accordingly yet
In the case where dividing multiple, subdivision higher frequency signal and the requirement for reducing sample frequency equipment.
The above examples are only used to illustrate the technical scheme of the present invention and are not limiting, although referring to preferred embodiment to this hair
It is bright to be described in detail, those skilled in the art should understand that, it can modify to technical solution of the present invention
Or equivalent replacement should all cover without departing from the objective and range of technical solution of the present invention in claim of the invention
In range.Technology not described in detail in the present invention, shape, construction portion are well-known technique.
Claims (6)
1. a kind of phase subdivision method based on wavelet transformation characterized by comprising
The optical interference signal that moving grating and fixed grating are formed is converted into electric signal, and the electric signal is adopted
Sample obtains sampled data；
Sampled data progress wavelet transformation is obtained into the instantaneous frequency of each sampled point, each section of sampled point is fitted and is obtained
To first frequency curve；
It determines the intermediate frequency in first frequency curve between adjacent both ends point, and the intermediate frequency between each two-end-point is clicked through
Row fitting obtains optimization frequency curve, and the sampled point between two-end-point is distributed according to the frequency curve of fitting；
Error-detecting is carried out to optimization frequency curve, and carries out error compensation, obtains the optimization frequency of sampled point；
After calculating begins to pass through time Δ t from time t, instantaneous frequency f (the t+ Δ t), if by between the time at place time point
The phase obtained after Δ t is 2 π/n, and counting N is carried out while calculating time interval Δ t, every to calculate a Δ t expression signal
Phase have passed through 2 π/n；
The distance of the moving grating movement is calculated according to movement relation.
2. a kind of phase subdivision method based on wavelet transformation according to claim 1, which is characterized in that the movement light
Grid are mounted on a sports platform, and the distance of the moving grating movement is the distance of sports platform movement.
3. a kind of phase subdivision method based on wavelet transformation according to claim 2, which is characterized in that described to described
Electric signal is sampled, and sampled data is obtained, comprising:
It carries out carrying out small echo to the electric signal after flexible translation obtains a series of wavelet sequences as basic function using morlet function
Transformation, extracts the modulus maximum of the electric signal finally to obtain the instantaneous frequency of signal.
4. a kind of phase subdivision method based on wavelet transformation according to claim 3, which is characterized in that further include to frequency
The frequency of inflection point of rate variation optimizes, and the method that the frequency to inflection point optimizes includes by inflection point punishment at before two
Two half parts are respectively processed afterwards, and first half is calculated by preceding sampled point, and rear part is calculated by post-sampling point.
5. a kind of phase subdivision method based on wavelet transformation according to claim 4, which is characterized in that further include to two
The signal frequency at end optimizes, and the method that the signal frequency to both ends optimizes is by the number of forward terminal, aft terminal
According to giving up, extended by the frequency and difference on the frequency of neighbouring sample point.
6. a kind of phase subdivision method based on wavelet transformation according to claim 5, which is characterized in that when calculating described
Between interval of delta t when, the signal frequency set in the time interval Δ t is constant, obtains 2 π of phase change/n time T=1/
(n*f (i)), wherein n is the multiple of subdivision, and f (i) is current frequency, obtains the frequency f (j) by time T, and then obtains frequency
The variation function of rate changes function according to frequency and acquires 2 π of phase change/n time Δ t.
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