Instantaneous microwave frequency measuring device and method based on dispersion Fourier transform
Technical Field
The invention belongs to the field of microwave photonics, and particularly relates to an instantaneous microwave frequency measurement technology based on dispersion Fourier transform time stretching frequency reduction.
Background
The microwave/millimeter wave technology is more and more widely applied to the aspects of national defense science and technology, microwave communication, industrial and agricultural production, daily life and the like, particularly in the fields of electronic warfare, radar early warning, wireless communication, space communication and the like. With the gradual expansion of microwave operating frequency in various application fields to high frequency band (even up to 300GHz), the real-time measurement and analysis of microwave signals by using the traditional frequency measurement technology in electric domain is not satisfactory due to the limitation of electronic bottleneck and instantaneous bandwidth. The development of a microwave signal frequency measurement technology suitable for the microwave signal frequency measurement technology is particularly important for realizing broadband, multi-tone, real-time and high-precision microwave frequency measurement.
At present, in addition to the conventional frequency sweep measurement technology in the electrical domain, the method for measuring microwave frequency attracts attention because the frequency measurement technology based on microwave photons has the advantages of large bandwidth, light weight, small loss and strong anti-electromagnetic interference capability. The microwave photon-based frequency measurement technology mainly comprises the following steps: frequency-space mapping methods (B.Luo, W.Pan, X.H.Zou, L.S.Yan, and B.Luo, "Photonic Microwave frequency mapping with high-coding-frequency digital outputs and large-frequency mapping," IEEE photon. J.5(5),5501906 (2013)), frequency-time mapping methods (L.V.T.Nguyen, "Microwave frequency mapping for small-frequency Microwave frequency mapping," IEEE photon. technique.21 (10), and 644(2009)), frequency-amplitude mapping methods (M.L.Bura, X.642, M.Li, L.Ch., J.Aware and Aware. frequency mapping, "Microwave frequency and amplitude mapping" W.2016, W.M.27, W.S.frequency mapping, Z.2016, and Z.2016 (2016, K.M.M.642, K.Q.L.Chystork, J.J.A, and J.A.S.sub.M.M.M.M.M.K.M.M.K., K.K.K.K.J.J.J.J.A.J.A.S.J.S.M.M.M.M.M.M.M.M.M.642, W.M.M.M.M.M.M.M.M.M.M.M.M.M.M.M.M.M.M.M.M.M.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A. Pat. No. 1, W.M.M.M.M.M.M.M.M.M.M.M.M.M.M.M.M.A.A.A. A. 1, and S.M.M.M.M.M.M.M.M.A.M.M.A.A.A. A. A.A. A. 15, and S.A. A. 98, and S. A. 98, and S. A. 98, and S. A.. The microwave frequency is mapped to different positions or channels in the space by a frequency-space mapping method, so that the microwave frequency is measured, the principle of the scheme is simple, but the scheme is limited by the bandwidth of the space or the channels, the measurement precision is not high, and the level is GHz; the frequency-time mapping method is characterized in that the microwave frequency to be measured is obtained by calculating relative delay amount by utilizing the principle that different microwave frequency components pass through the same dispersion medium to obtain different delay amounts, and the measurement range and the measurement precision are related to and mutually restricted with the selected dispersion medium; the microwave frequency measurement technology based on the frequency-amplitude mapping method maps the microwave frequency with the received microwave or light wave power, the scheme has good reconfigurability, the frequency measurement precision reaches 0.2GHz, but the problem of mutual restriction relation between the frequency range and the precision is also faced, and meanwhile, the scheme cannot measure multi-tone signals. Recently, there have been proposed studies to realize Measurement of a frequency of a microwave to be measured by analyzing a minimum mixing frequency component using an optical frequency comb mixing technique (g.q.hu, t.mizuguchi, x.zhao, t.minamikawa, t.mizuno, y.l.yang, c.li, m.bai, z.zheng, and t.yasui, "Measurement of absolute frequency of continuous-wave radiation in real time using a free-running, dual-wave length mode-locked, erb-measured fiber laser," sci.7, 42082(2017)), which has advantages of a wide Measurement frequency range, high Measurement accuracy and real-time Measurement, but has disadvantages of a Measurement dead zone, two or more optical frequency combs and incapability of realizing multi-tone microwave Measurement.
At present, there is a need to develop a microwave frequency measurement method that can meet the requirements of broadband, multi-tone, real-time and high-precision microwave signal frequency measurement, reduce the number of optical frequency combs and overcome the measurement blind area. In order to solve the problems, the invention adopts a dispersion Fourier transform time stretching method, microwave signals before and after frequency reduction are subjected to dispersion Fourier transform time stretching and frequency mixing with photons of the same optical frequency comb, so that the frequency mixing of the same microwave signal to be measured and two different multiple-frequency optical frequency combs is equivalent, namely, double-optical frequency comb frequency mixing is realized by using the single optical frequency comb, and broadband, high-precision, blind-area-free and multi-tone microwave frequency instantaneous measurement is realized according to the frequency cross-reference relationship between frequency mixing components.
Disclosure of Invention
The present invention is directed to solving the above problems of the prior art. A method is presented. The technical scheme of the invention is as follows:
an instantaneous microwave frequency measurement device based on dispersive fourier transform, comprising: the system comprises an ultra-short optical pulse light source, a dispersion Fourier change module I, an electro-optical intensity modulator, an optical power divider, a dispersion Fourier change module II, a nonlinear photon mixing module, a photoelectric detector I, a photoelectric detector II, a microwave power coupler and a spectrum analysis module; the ultra-short optical pulse light source is sequentially connected with a dispersion Fourier change module I and an electro-optical intensity modulator, one path of the electro-optical intensity modulator is connected with a photoelectric detector I through an optical power divider, the other path of the electro-optical intensity modulator is connected with a dispersion Fourier change module II, the dispersion Fourier change module II is connected with a microwave power coupler through a nonlinear photon frequency mixing module and the photoelectric detector II in sequence, the photoelectric detector I is also connected with the microwave power coupler, and the microwave power coupler is connected with a spectrum analysis module after being coupled; the ultra-short light pulse light source is used for generating ultra-short light pulses, the dispersion Fourier change module I is used for realizing pulse width dispersion time stretching and broadening of the ultra-short light pulses, the electro-optical intensity modulator is used for loading microwave signals to be detected onto stretched optical pulses, the optical power splitter is used for splitting the optical signals into two parts, the dispersion Fourier change module II is used for further dispersing time stretching and broadening the optical pulses modulating the microwave signals to be detected, the nonlinear photon mixing module is used for realizing the nonlinear effect of light, the photoelectric detector I is used for performing photoelectric conversion on the optical signals, the photoelectric detector II is used for performing photoelectric conversion on the optical signals, the microwave power coupler is used for coupling two paths of microwave signals, and the spectrum analysis module is used for analyzing the frequency spectrums of the electrical signals.
Further, the instantaneous microwave frequency measuring device based on the dispersion Fourier transform is characterized in that the ultrashort pulse light source, the dispersion Fourier change module I, the electro-optical intensity modulator, the optical power splitter, the dispersion Fourier change module II, the nonlinear photon mixing module, the photoelectric detector I and the photoelectric detector II are connected through an optical path;
furthermore, the photoelectric detector I, the photoelectric detector II, the microwave power coupler and the spectrum analysis module are in circuit connection.
Further, the instantaneous microwave frequency measuring device based on the dispersion fourier transform is characterized in that the dispersion fourier transform module is a dispersion medium, can be a single-mode fiber or a fiber grating, and is used for realizing the stretching and broadening of the optical pulse width of the ultrashort pulse light source.
Further, the instantaneous microwave frequency measuring device based on the dispersion fourier transform is characterized in that the nonlinear photon frequency mixing module realizes photon frequency mixing by utilizing nonlinear effects such as cross gain modulation effect, four-wave frequency mixing effect and the like, and adopts a high nonlinear optical fiber and a nonlinear semiconductor optical amplifier.
A measuring method based on the device of claims 1-4, characterized by comprising the following steps:
the ultra-short optical pulse light source generates linear chirped optical pulses through the dispersion Fourier transform module I, pulse width broadening is realized, microwave signals to be detected are loaded onto the linear chirped optical pulses through the electro-optical intensity modulator, the optical signals after passing through the dispersion Fourier transform module II realize frequency mixing of secondary time stretching microwave signals and optical frequency combs by utilizing the nonlinear frequency mixing module, at the moment, the microwave signals to be detected before and after secondary time frequency reduction stretching are mixed with photons of the same optical pulses, so that frequency mixing of the same microwave signals and two different multiple-frequency optical frequency combs is equivalently formed, namely double-optical frequency comb frequency mixing is realized by utilizing a single optical frequency comb, and the frequency of the microwave signals to be detected is finally obtained by analyzing the frequency cross-reference relationship between the coupled mixed frequency down-conversion signals according to the frequency cross-reference relationship between frequency mixing components.
Further, the measuring method is characterized in that the frequencies of the microwave signals to be measured before and after the secondary time stretching frequency reduction through the dispersion Fourier transform module II are respectively fsAnd fs/M, the frequency of the microwave signal to be measured is fsM is the stretching multiple of dispersion time, namely the ratio of the total dispersion of the link dispersion Fourier transform modules I and II to the dispersion of the dispersion Fourier transform module II, the process is equivalent to the frequency mixing of the same microwave signal to be measured and two different multiple frequency optical frequency combs, the repetition frequencies of the equivalent optical frequency combs are respectively fr1And fr2And satisfy fr2=M*fr1All frequencies obtained are less than fr2Are respectively fa、fb、fcAnd fdWherein f isa+fb=fr1,fc+fd=fr2,fr2-fr1=Δf;
If a positive integer N and a mixing signal f are presentaSo that | fa-fcN × Δ f and | fb-fdIf | (N +1) × Δ f holds simultaneously, the frequency f to be measureds=N×fr1+fa(ii) a If a positive integer N and a mixing signal f are presentaSo that fa+fcIf NxDeltaf is true, the frequency of the microwave signal to be measured is the frequencyRate fs=N×fr1+fa。
Further, the measurement method is characterized in that the repetition frequency is fr1The optical frequency comb generated by the ultra-short optical pulse light source can be represented by a series of Gaussian pulse series superposition, and is expressed as follows in the frequency domain:
wherein f isr1=1/Tr1,Tr1And T0Full width at half maximum, E, of pulse period and Gaussian light pulse, respectively0For the amplitude of the light source, f is the frequency of the light pulse, δ (f) is the frequency domain representation of the impulse function, and n is an integer. When the optical fiber is a single-mode optical fiber, the ultra-short optical pulse is subjected to dispersion Fourier transform by the dispersion Fourier transform module I to realize wavelength-time mapping, and the output chirped optical pulse can be expressed in a frequency domain as follows:
wherein L is1Length of single mode optical fibre, beta2J is a complex number for its group velocity dispersion coefficient;
frequency f by an electro-optical intensity modulatorsThe microwave signal to be measured is modulated onto the chirped optical pulse, and under the condition of small signal approximation, the modulated optical signal can be expressed as:
where m is the modulation coefficient and the symbol "+" is the convolution operation.
The modulated light pulse passes through a dispersion Fourier transform module II, namely the length of the modulated light pulse is L2After the single-mode fiber is subjected to dispersion Fourier transform, the output spectrum of the single-mode fiber is as follows:
it can be expressed in the time domain as:
wherein M ═ L1+L2)/L1Is the time stretch multiple, t is the time, at this time, the original frequency is fsIs down-converted to f by dispersive Fourier transform stretchingsMicrowave signal of/M.
The invention has the following advantages and beneficial effects:
1) microwave signals before and after the secondary time stretching frequency reduction through dispersion Fourier transform are mixed with photons of the same optical frequency comb, so that the microwave signals to be measured are equivalent to the mixing of the same microwave signal to be measured and two different multiple frequency optical frequency combs, namely, the double optical frequency comb mixing is realized by utilizing a single optical frequency comb; by analyzing the frequency cross-reference relationship between the mixing signals, the microwave signal frequency measurement with wide frequency, multi-tone, real time and high precision is realized;
2) compared with a microwave frequency measurement method based on a frequency-parameter mapping method, the microwave signal frequency measurement error of the method is reduced by 8 orders of magnitude, the measurement resolution is improved by 8 orders of magnitude, and the measurement range is wider;
3) compared with the traditional optical frequency comb frequency mixing method, the method overcomes the key technical problem of measurement blind areas in the traditional optical frequency comb frequency mixing method through the frequency cross-reference relation, does not need a plurality of optical frequency comb light sources, and has a simple measurement structure.
Drawings
FIG. 1 is a schematic block diagram of a preferred embodiment instantaneous microwave frequency measurement system provided by the present invention;
FIG. 2 is a schematic diagram of a frequency spectrum of a mixing signal in a single frequency measurement according to an embodiment of the present invention;
FIG. 3 is a schematic diagram of a spectrum of a mixing signal in a multi-tone signal measurement according to an embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be described in detail and clearly with reference to the accompanying drawings. The described embodiments are only some of the embodiments of the present invention.
The technical scheme for solving the technical problems is as follows:
a method for measuring instantaneous microwave frequency based on dispersive Fourier transform time stretching frequency reduction comprises the following steps:
(1) repetition frequency of fr1The ultra-short pulse light source generates linear chirped light pulses through the dispersion Fourier change module I;
(2) will have a frequency fsThe microwave signal to be tested is loaded on the linear chirped light pulse through the electro-optical intensity modulator, the modulated light signal is divided into two parts through the optical power divider, one light beam is subjected to photoelectric conversion through the photoelectric detector I to realize photon frequency mixing of the microwave signal to be tested and the light pulse, the other light beam is further stretched through the dispersion Fourier change module II to realize photon frequency mixing of the stretched microwave signal to be tested and the light pulse through the nonlinear photon frequency mixing module;
(3) the microwave signal to be measured before and after the secondary time stretching frequency reduction through the dispersion Fourier transform module II is mixed with the photons of the same optical pulse, and the frequency of the microwave signal to be measured before and after the time stretching frequency reduction through the dispersion Fourier transform module II is respectively fsAnd fsM is the dispersion time stretch multiple (the ratio of the total dispersion of the link dispersion Fourier transform modules I and II to the dispersion of the dispersion Fourier transform module II), the process is equivalent to the mixing of the same microwave signal to be measured and two different multiple-frequency optical frequency combs, the repetition frequencies of the equivalent optical frequency combs are respectively fr1And fr2And satisfy fr2=M*fr1So as to be equivalent to the frequency mixing of the same microwave signal and two different heavy frequency optical frequency combs;
(4) the electric signals output from the two photoelectric detectors are combined by the electric coupler and enter the spectrum analysis module to obtain the frequency less than fr2Of mixed signals of, respectively, fa、fb、fcAnd fdWherein f isa+fb=fr1,fc+fd=fr2;
(5) If a positive integer N and a mixing signal f are presentaSo that | fa-fcN × Δ f and | fb-fdIf | (N +1) × Δ f holds simultaneously, the frequency f to be measureds=N×fr1+fa(ii) a If a positive integer N and a mixing signal f are presentaSo that fa+fcIf NxDeltaf holds, the frequency f to be measureds=N×fr1+fa. I.e. a frequency cross-reference relationship.
FIG. 1 is a schematic block diagram of an instantaneous microwave frequency measurement system based on dispersive Fourier transform time stretch downconversion according to the present invention: the optical pulse output by the ultrashort pulse light source is subjected to prestretching pulse broadening through a dispersion Fourier transform module I, a microwave signal to be detected is loaded on the stretched optical pulse by using an electric light intensity modulator, a modulation signal is divided into two parts through an optical beam splitter, one part of the modulation signal enters a photoelectric detection I, the other part of the modulation signal enters a dispersion Fourier transform module II and a nonlinear photon mixing module to be subjected to reteretching and photon nonlinear mixing, so that the microwave signal to be detected before and after the frequency reduction through the secondary time stretching of the dispersion Fourier transform module II is mixed with photons of the same optical pulse, the photoelectric detection is carried out through a photoelectric detector I and a photoelectric detector II, the output electric signal enters a spectrum analysis module through the combination of a microwave power coupler, and all the frequencies of which are less than f are obtainedr2Of mixed signals of, respectively, fa、fb、fcAnd fdWherein f isa+fb=fr1,fc+fd=fr2If there is a positive integer N, so that | fa-fcN × Δ f and | fb-fdIf | (N +1) × Δ f holds simultaneously, the frequency f to be measureds=N×fr1+fa(ii) a If a positive integer N is present, such that fa+fcIf NxDeltaf holds, the frequency f to be measureds=N×fr1+fa。
The principle of the instantaneous microwave frequency measuring method based on the dispersion Fourier transform time stretching frequency reduction of the invention is as follows:
repetition frequency of fr1The optical frequency comb generated by the ultra-short optical pulse light source can be represented by a series of Gaussian pulse series superposition, and is expressed as follows in the frequency domain:
wherein f isr1=1/Tr1,Tr1And T0Full width at half maximum, E, of pulse period and Gaussian light pulse, respectively0For the amplitude of the light source, f is the frequency of the light pulse, δ (f) is the frequency domain representation of the impulse function, and n is an integer. After the ultrashort optical pulse is subjected to dispersion fourier transform by a dispersion fourier transform module i (taking a single-mode fiber as an example), wavelength-time mapping is realized, and the output chirped optical pulse can be represented in a frequency domain as follows:
wherein L is1Length of single mode optical fibre, beta2J is a complex number for its group velocity dispersion coefficient.
Frequency f by an electro-optical intensity modulatorsThe microwave signal to be measured is modulated onto the chirped optical pulse, and under the condition of small signal approximation, the modulated optical signal can be expressed as:
where m is the modulation coefficient and the symbol "+" is the convolution operation.
The modulated light pulse passes through a dispersion Fourier transform module II (for example, the length is L)2Single mode fiber dispersion) fourier transform, the output spectrum is:
it can be expressed in the time domain as:
wherein M ═ L1+L2)/L1Is the time stretch factor, t is the time. At this time, the original frequency is fsIs down-converted to f by dispersive Fourier transform stretchingsHowever, as can be seen from the formulas (3) and (4), the spectral components of the/M microwave signal are not changed, and therefore, the dispersive fourier transform, stretching and frequency-down conversion microwave signal cannot be directly mixed with photons of the optical frequency comb by photoelectric detection.
The modulated light pulse is detected by a photoelectric detector I, and the microwave signal before stretching and frequency reduction is finished and the repetition frequency is fr1The photons of the optical frequency comb are mixed. As can be seen from equation (3), the frequency components involved in mixing mainly include: f. of0+nfr1、f0+nfr1+fsAnd f0+nfr1-fsThe frequency mixing is realized through heterodyne beat frequency, and the frequency of frequency mixing components is as follows:
fMIX1=|fs-nfr1| (6)
as can be seen from equation (5), the stretched optical pulse envelope signal has a frequency fsThe original ultra-short light pulse has the frequency f after the microwave signal of/M and the original ultra-short light pulse pass through the nonlinear photon frequency mixing modulesThe microwave signal of/M is modulated, and the modulation process can be simplified as follows:
where gamma is the nonlinear mixing efficiency coefficient.
The modulated ultrashort optical pulse is detected by a low-frequency photoelectric detector, and the photon mixing of the stretched and frequency-reduced microwave signal and the optical frequency comb is completed. As can be seen from equation (7), the frequency components involved in mixing mainly include: f. of0+nfr1、f0+nfr1+fs(ii) M and f0+nfr1-fsand/M, the mixing frequency obtained by heterodyne beat frequency among the two is as follows:
multiplying both sides of equation (8) by M simultaneously is:
MfMIX2=|fs-nMfr1|=|fs-nfr2| (9)
wherein f isr2=Mfr1. In this case, the repetition frequency can be equivalent to fr2With an optical frequency of fsPhotonic mixing of the microwave signal. The combination of equations (6) and (9) can be considered as a comb of optical frequencies of different repetition frequencies and a frequency fsThe photon frequency mixing of the microwave signal can realize that the frequency mixing effect of the double optical frequency comb can be generated only by a single optical frequency comb.
At the obtained mixing signal fmix1=|fs-nfr1I and fmix2=|fs-nfr2In |, the search frequency is less than fr2Of mixed signals of, respectively, fa、fb、fcAnd fdWherein f isa+fb=fr1,fc+fd=fr2If present, the positive integer N and the mixing signal faSo that | fa-fcN × Δ f and | fb-fdIf | (N +1) × Δ f holds simultaneously, the frequency f to be measureds=N×fr1+fa(ii) a If a positive integer N and a mixing signal f are presentaSo that fa+fcIf NxDeltaf holds, the frequency f to be measureds=N×fr1+fa. I.e. a frequency cross-reference relationship.
Example 1
Single frequency microwave signal measurement
Supposing that the frequency of the microwave signal to be measured is 55.5GHz, the repetition frequency f of the ultra-short optical pulse light sourcer1Respectively 4.01GHz, adjusting the lengths of the single-mode fibers at the two ends to ensure that the stretching ratio M is 1.032, and then obtaining the equivalentOptical frequency comb repetition frequency fr2At 4.137GHz, the spectral resolution of the spectral analysis module is 0.5 MHz. As shown in fig. 2, the condition f is obtaineda+fb=fr1And fc+fd=fr2Of the mixing signals of frequency fa=3.37GHz、fb=0.64GHz、fc1.719GHz and fd2.418 GHz. At this time, there is a positive integer N of 13, such that | fa-fcN × Δ f and | fb-fdIf | (N +1) × Δ f, then the frequency f to be measureds=N×fr1+fa(13 × 4.01+3.37) GHz ═ 55.5 GHz. The measured microwave frequency value is consistent with the frequency of the microwave signal to be measured, and the accuracy of the instantaneous microwave frequency measuring method is verified. Secondly, the frequency of the microwave to be measured is 55.5GHz just in the measurement blind zone of the traditional double-optical-frequency comb frequency measurement method, namely 13.5 xfr1<fs<13.5×fr2,54.135GHz<55.5GHz<55.8495GHz), through experimental verification, the invention further provides the instantaneous microwave frequency measurement method based on dispersion Fourier transform time stretching frequency reduction, which can overcome the problem of frequency measurement blind zone in the traditional scheme, and only needs 1 optical frequency comb.
Example 2
Multi-tone microwave signal measurement
Assuming that the frequency of the microwave signal to be measured is 55.5GHz and 55.502GHz, the repetition frequency f of the ultra-short light pulse light sourcer1The lengths of the single-mode fibers at the two ends are respectively adjusted to 4.01GHz, so that the stretching multiple M is 1.032, and the repetition frequency f of the equivalent optical frequency comb is equal tor2At 4.137GHz, the spectral resolution of the spectral analysis module is 0.5 MHz. As shown in fig. 3, the condition f is obtaineda1+fb1=fr1And fc1+fd1=fr2Of the mixing signals of frequency fa1=3.37GHz、fb1=0.64GHz、fc11.719GHz and fd12.418GHz, satisfies fa2+fb2=fr1And fc2+fd2=fr2Of the mixing signals of frequency fa2=3.372GHz、fb2=0.638GHz、fc21.721GHz and fd22.416 GHz. At this time, there is a positive integer N of 13, such that | fa1-fc1|=N1x.DELTA.f and | fb1-fd1|=(N1+1) x Δ f, the frequency f to be measureds=N1×fr1+fa1(13 × 4.01+3.37) GHz ═ 55.5 GHz. Presence of a positive integer N213, make | fa2-fc2|=N2x.DELTA.f and | fb2-fd2|=(N2+1) x Δ f, the frequency f to be measureds=N2×fr1+fa(13 × 4.01+3.372) GHz 55.502 GHz. If the measured microwave frequency value is consistent with the frequency of the multi-tone microwave signal to be measured, the instantaneous microwave frequency measuring method based on dispersion Fourier transform time stretching frequency reduction can accurately measure the frequency of the multi-tone microwave signal.
The systems, devices, modules or units illustrated in the above embodiments may be implemented by a computer chip or an entity, or by a product with certain functions. One typical implementation device is a computer. In particular, the computer may be, for example, a personal computer, a laptop computer, a cellular telephone, a camera phone, a smartphone, a personal digital assistant, a media player, a navigation device, an email device, a game console, a tablet computer, a wearable device, or a combination of any of these devices.
It should also be noted that the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising an … …" does not exclude the presence of other like elements in a process, method, article, or apparatus that comprises the element.
The above examples are to be construed as merely illustrative and not limitative of the remainder of the disclosure. After reading the description of the invention, the skilled person can make various changes or modifications to the invention, and these equivalent changes and modifications also fall into the scope of the invention defined by the claims.