CN114414048B - Device and method for improving modulation spectrum measurement precision - Google Patents
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Abstract
The invention discloses a device and a method for improving modulation spectrum measurement precision, comprising a narrow linewidth laser, an electro-optical modulator, a spectrum analysis module, a microwave signal source and a data acquisition and control module, wherein the narrow linewidth laser, the electro-optical modulator and the spectrum analysis module are sequentially and optically connected, the microwave signal source is electrically connected with the electro-optical modulator, and the data acquisition and control module is respectively connected with the microwave signal source and the spectrum analysis module by adopting a data bus. And measuring spectral lines of the narrow linewidth optical carrier by using a spectrometer as a system basis function, and then constructing an actual measurement spectral line model by using the system basis function to fit the actual measurement spectrum to obtain the position and the amplitude of each spectral line of the spectrum to be measured. The invention solves the problem of larger measurement error of the modulation spectrum caused by the superposition of the spectral line intensities under the condition that the spectral lines to be resolved are close by the limitation of the resolution of the grating spectrum analysis in the spectrum measurement process, and improves the measurement accuracy of the modulation spectrum.
Description
Technical Field
The invention relates to the field of spectrum resolution enhancement, in particular to a device and a method for improving modulation spectrum measurement precision.
Background
In the spectrum acquisition process, due to the natural broadening of spectral lines, the influence of instrument response functions and other factors, spectral data bands are overlapped, the signal to noise ratio is reduced, and the spectrum is expressed on the functions, namely, the observation result is the result of the composite convolution of a real signal and various convolution kernel functions. According to the Rayleigh criterion, when two spectral lines with the same amplitude are synthesized into intensity which is distributed in a saddle shape and the intensity valley value is less than or equal to 81% or 73% of the intensity peak value, the spectral lines can be just or can be distinguished; however, when the spectrum line amplitude difference is larger, the spectrum line with lower amplitude is completely submerged in the spectrum line with higher amplitude, and at the moment, the judgment is carried out through the intensity peak-valley value of the Rayleigh criterion, the error of measuring the spectrum line is larger, and even the error occurs.
Since the convolution process spreads the spectrum and causes spectral lines to overlap, distorting the measured spectrum, recovering and recovering the true spectral line from the distorted spectral line to improve spectral resolution is a deconvolution problem. If the response function of the instrument is known, the method is a conventional deconvolution problem, and the conventional deconvolution method at present mainly comprises a frequency domain deconvolution algorithm based on Fourier transform and a spatial domain algorithm based on iterative deconvolution; if the response function of the instrument is unknown, the blind deconvolution problem is solved.
The conventional deconvolution needs to define an accurate convolution kernel function, and because the actually measured spectrum is a composite convolution result of a real signal and various convolution kernel functions, the actual spectrum is influenced by various factors including instruments, environments and the like, and a commonly applicable kernel function is difficult to propose. Whereas blind deconvolution, while solving the problem of difficulty in finding a kernel function, is difficult to meet the requirement of repeatable results. In addition, due to the influence of noise and inaccuracy of the kernel function, the deconvolution method can only reduce the broadening of the measured spectral line as much as possible so as to distinguish each spectral peak in the spectral line, but cannot completely eliminate the influence of the spectral peak on the real spectral line intensity. In an application occasion (such as measurement of a modulation spectrum) where the spectrum line intensity at a certain specific wavelength in a spectrum needs to be measured accurately, the deconvolution method has limited effect of improving the spectrum line intensity measurement precision, and particularly when the positions of two spectrum lines to be measured are very close, the peak value error of the spectrum line intensity to be measured obtained by the deconvolution method is still larger and even the mutually submerged spectrum lines cannot be distinguished.
Disclosure of Invention
In order to solve the problem of low measurement accuracy of the modulation spectrum caused by the reasons, the invention provides a device and a method for improving the measurement accuracy of the modulation spectrum. And measuring spectral lines of the narrow linewidth optical carrier by using a spectrometer as a system basis function, and then constructing an actual measurement spectral line model by using the system basis function as the basis function to fit the actual measurement spectrum to obtain the position and the amplitude of each spectral line of the spectrum to be measured. The system basis function obtained by the method simultaneously comprises the influence of various factors such as instruments, environments and the like on the spectral line, and the real spectral line is recovered in a fitting rather than deconvolution mode, so that the influence of inaccuracy of the kernel function and noise on a recovery result is greatly reduced, and the measurement accuracy of the spectral line can be improved.
The device for improving the modulation spectrum measurement precision comprises a narrow linewidth laser, an electro-optical modulator, a spectrum analysis module, a microwave signal source and a data acquisition and control module, wherein the narrow linewidth laser, the electro-optical modulator and the spectrum analysis module are sequentially and optically connected, the microwave signal source is electrically connected with the electro-optical modulator, and the data acquisition and control module is respectively connected with the microwave signal source and the spectrum analysis module through a data bus. The data acquisition and control module sets the frequency and power output by the microwave signal source through the bus, the microwave signal is loaded onto the optical carrier through the electro-optical modulator to form a modulated optical signal to be incident to the spectrum analysis module, and the data acquisition and control module acquires modulated spectrum data through the bus.
A method of improving the accuracy of modulation spectroscopy measurements, comprising the steps of:
s1: the data acquisition and control module controls the microwave signal source to output microwave signals with specific frequency and power, and acquires actual measurement spectrum data x (lambda) through the spectrum analysis module;
s2: the data acquisition and control module controls the microwave signal source not to output microwave signals, and obtains no-load spectrum data h (lambda) of the electro-optic modulator under no-load through the spectrum analysis module;
s3: given the number N of spectral peaks in advance, if the peak position lambda of the ith spectral peak is known i (i=1, …, N), steps S4 and S5 are skipped directly to step S6;
s4: observing the noise floor of the measured spectrum data x (lambda), obtaining gradient data Dx (lambda) by solving the gradient of the measured spectrum data which is 20dB higher than the noise floor, and searching the data points of which the signs of the data points at two adjacent sides in the Dx (lambda) are changed from positive to negative, wherein the corresponding lambda is taken as the peak position lambda of the ith spectrum peak i (i=1, …, M) to obtain M pieces of peak position information in total;
s5: if M>Directly enter step S6, otherwise, add N-M peak position information based on M peak position information obtained in step S4, corresponding peak position lambda N+p The value of (p=1, …, N-M) can be determined from λ i (i=1, …, M) to obtain new peak position information λ i (i＝1,…,N)；
S6: peak position lambda for each spectral peak i Applying a deviation Deltalambda i (i=1, …, N) to obtain a new peak position λ of the spectral peak i +Δλ i The method comprises the steps of carrying out a first treatment on the surface of the Constructing an estimate of the measured spectrum x (λ):
wherein a is i For peak position lambda of spectral line i +Δλ i Amplitude value of delta [ lambda- (lambda) i +Δλ i )]Is a dirac function for λ;
s7: by means of an optimization algorithm combined with least squares fitting
(wherein a= (a) 1 ,…,a N )，ΔΛ＝(Δλ 1 ,…,Δλ N ) N is the number of points of the spectrum data) minimum is an objective function to obtain peak position lambda of each spectrum peak i +Δλ i And the corresponding amplitude value a i ；
S8: peak position lambda obtained by S7 i +Δλ i And amplitude value a i (i=1, …, N) to obtain a modulation spectrum
Further, in the step S7, the optimization algorithm is a genetic algorithm, and the specific steps of solving the peak position deviation ΔΛ of the spectrum peak and the corresponding amplitude value a by combining the genetic algorithm with the least square fitting method are as follows:
t1: let ΔΛ= (Δλ) 1 ,…,Δλ N ) As a search variable of the genetic algorithm, the dimension is N, and a search range is limited according to actual conditions;
t2: encoding delta lambda to generate a chromosome;
t3: randomly generating an initial population with a population size G in a search range, wherein chromosomes of each individual in the population correspond to different peak position deviation amounts delta lambda g (g＝1,…,G)；
T4: ΔΛ of the g-th individual g Substitution into
Then solving the best using the Levenberg-Marquardt Method, L-M MethodThe small-square fitting problem yields ΔΛ=ΔΛ g Amplitude value A at the time g Sum of squares of residuals F g And combining-F g As fitness value of the individual;
t5: repeating the step T4 until the fitness value of all individuals in the population is calculated;
t6: recording ΔΛ of the optimal individual (the individual with the largest fitness value) and an amplitude value a obtained by least squares fitting at the ΔΛ;
t7: selecting a better individual 'survived' in the population by adopting a roulette method, and performing crossing and mutation operation on chromosomes of the better individual 'survived' to generate a next generation population;
t8: and repeating the steps T4-T7 until the relative change of the optimal fitness value is lower than the set value, and then outputting the delta lambda of the optimal individual in the last generation and the amplitude value A obtained by least square fitting under the delta lambda.
Further, in the step S4, the change from positive to negative is generally made up of more than 2 consecutive positive and more than 2 consecutive negative, such as "positive, negative and negative".
Further, in the step S6, δ [ λ - (λ) i +Δλ i )]And can also be replaced by a linear function of the microwave signal output by the microwave signal source.
Compared with the prior art, the invention has the beneficial effects that:
1. the invention uses the optical carrier spectrum acquired by the spectrum analysis module as the system basis function, thereby avoiding the difficulty of providing a universally applicable kernel function, and the system basis function simultaneously comprises the influence of various factors such as the line width of the optical carrier, an instrument, the environment and the like on spectral lines when measuring the modulation spectrum, and the response description of the optical instrument under different environments is more accurate.
2. Compared with a deconvolution method, the method provided by the invention has the advantages that the original spectral line is restored by adopting a fitting method, the influence of inaccuracy of a kernel function and noise on a restoration result is greatly reduced, and the influence of the line width of an optical carrier and the widening of a system basis function can be completely eliminated, so that the resolution of a modulation spectrum can be improved.
3. In the application occasion of needing to measure the intensity of a specific spectral line in the modulation spectrum, the invention fully utilizes the information of the whole observation spectrum, obtains the intensity value of the specific modulation spectral line from the fitting result, and does not only utilize one spectral peak value of the observation spectrum, thereby improving the measurement accuracy of the spectral peak value of the modulation spectrum. And the intensity relation among all the modulation spectral lines is integrated into a fitting model through theoretical deduction, so that the measurement error can be further reduced.
4. The invention provides two modes for acquiring the peak position of the initial spectrum peak (the known peak position of the spectrum peak and the obtained spectrum is obtained from the actually measured spectrum by an algorithm) and the corresponding solving algorithm thereof, thereby increasing the flexibility. For the condition of the known peak position of the spectrum peak, when a fitting model is established, the relation constraint information among modulation spectral lines can be fully utilized for a specific modulation system, and the measurement precision is improved; the algorithm is used for obtaining the initial spectrum peak position from the actually measured spectrum, so that the theoretical derivation process can be avoided, and the method has certain universality.
Drawings
FIG. 1 is a schematic diagram of an apparatus for improving the accuracy of modulation spectrum measurement according to the present invention.
FIG. 2 is a graph showing the result of recovering a modulation spectrum using the method of the present invention in example one.
FIG. 3 is a graph showing the result of recovering a modulation spectrum using the method of the present invention in example two.
Detailed Description
The present invention is further described below in conjunction with embodiments, which are merely some, but not all embodiments of the present invention. Based on the embodiments of the present invention, other embodiments that may be used by those of ordinary skill in the art without making any inventive effort are within the scope of the present invention.
Embodiments of the invention are further described below with reference to the drawings and mathematical derivations.
Example 1
The device for improving the modulation spectrum measurement precision comprises a narrow linewidth laser, an electro-optical modulator, a spectrum analysis module, a microwave signal source and a data acquisition and control module, wherein the narrow linewidth laser, the electro-optical modulator and the spectrum analysis module are sequentially and optically connected, the microwave signal source is electrically connected with the electro-optical modulator, and the data acquisition and control module is respectively connected with the microwave signal source and the spectrum analysis module through a data bus. The data acquisition and control module sets the frequency and power output by the microwave signal source through the bus, the microwave signal is loaded onto the optical carrier through the electro-optical modulator to form a modulated optical signal to be incident to the spectrum analysis module, and the data acquisition and control module acquires modulated spectrum data through the bus.
The device and the method of the invention can improve the measurement accuracy of the actually measured modulation spectrum of the known spectrum peak position. The frequency emitted by the laser is f 0 The optical carrier wave of the microwave signal source is modulated by an electro-optical modulator, and firstly, the data acquisition and control module controls the output frequency of the microwave signal source to be f m And then the data acquisition and control module controls the microwave signal source not to output the microwave signal and acquires the spectrum data of the spectrum analysis module to obtain the idle spectrum data h (lambda) of the electro-optic modulator under the idle condition.
For a particular electro-optic modulator, the position of its modulation sideband can be deduced, and the frequency of the modulation sideband of the electro-optic modulator in this embodiment is f 0 +nf m (n is an integer), if only positive and negative third-order sidebands are taken, the frequency of the modulation sideband is f 0 +nf m (n= -3, -2, …, 3). Converting it to a wavelength with λ=c/f to obtain peak positions of 7 spectral peaks, λ i (i＝1,…,7)。
Peak position lambda for each spectral peak i Applying a deviation Deltalambda i (i=1, …, 7) to obtain a new peak position λ of the spectral peak i +Δλ i The method comprises the steps of carrying out a first treatment on the surface of the Constructing an estimate of the measured spectrum x (λ):
wherein a is i For peak position lambda of spectral line i +Δλ i Amplitude value of delta [ lambda- (lambda) i +Δλ i )]Is a dirac function for λ. If the intensity relationship between the modulation sidebands is known, the method can be used for the comparison of a i Further restrictions are made to further increase the measurement accuracy, and the present embodiment does not consider the intensity relationship between modulation sidebands in order not to lose universality.
By means of an optimization algorithm combined with least squares fitting
(wherein a= (a) 1 ,…,a 7 )，ΔΛ＝(Δλ 1 ,…,Δλ 7 ) N is the number of points of the spectrum data) minimum is an objective function to obtain peak position lambda of each spectrum peak i +Δλ i And the corresponding amplitude value a i . The specific solving steps are as follows:
t1: let ΔΛ= (Δλ) 1 ,…,Δλ 7 ) As a search variable of the genetic algorithm, the dimension is 7, and the offset of the known modulation spectral line position is not larger than the magnitude of the sampling step length of the spectrometer, so that the search range is limited to (-0.1 nm,0.1 nm);
t2: encoding delta lambda to generate a chromosome;
t3: randomly generating an initial population with a population size of 100 in a search range, wherein chromosomes of each individual in the population correspond to different peak position deviation amounts delta lambda g (g＝1,…,100)；
T4: ΔΛ of the g-th individual g Substitution into
The least squares fitting problem is then solved with the Levenberg-Marquardt Method (L-M Method) to give ΔΛ=ΔΛ g Amplitude value A at the time g Sum of squares of residuals F g And combining-F g As fitness value of the individual;
t5: repeating the step T4 until the fitness value of all individuals in the population is calculated;
t6: recording ΔΛ of the optimal individual (the individual with the largest fitness value) and an amplitude value a obtained by least squares fitting at the ΔΛ;
t7: selecting a better individual 'survived' in the population by adopting a roulette method, and performing crossing and mutation operation on chromosomes of the better individual 'survived' to generate a next generation population;
t8: repeating the steps T4-T7 until the relative change of the continuous 20-generation optimal fitness value is lower than 10 -6 Then, ΔΛ of the optimal individual in the last generation and the amplitude value a obtained by least squares fitting at this ΔΛ are output.
Finally according to the obtained peak position lambda i +Δλ i And amplitude value a i (i=1, …, 7) to obtain a modulation spectrum
Fig. 2 is a comparison of the measured modulation spectrum of the present embodiment, where the wavelength of the optical carrier is 1550nm and the microwave modulation frequency fm is set to 1GHz, and the modulation spectrum recovered by the method of the present invention. It can be seen that the method successfully recovers the sidebands covered by the carrier wave and improves the spectral resolution.
Example two
The device and the method of the invention are used for improving the resolution and the measurement precision of the modulation spectrum. The difference from the first embodiment is that the peak position lambda of the spectrum peak of the modulation spectrum is not known in advance in the present embodiment i . The specific implementation process is as follows:
the frequency emitted by the laser is f 0 The optical carrier wave of the microwave signal source is modulated by an electro-optical modulator, and firstly, the data acquisition and control module controls the output frequency of the microwave signal source to be f m And then the data acquisition and control module controls the microwave signal source not to output the microwave signal and acquires the spectrum data of the spectrum analysis module to obtain the idle spectrum data h (lambda) of the electro-optic modulator under the idle condition.
Given the number of spectral peaks 5 to be resolved from the measured modulation spectrum, since the spectral peak position information is not known, the spectral peak position information needs to be obtained from the measured spectral data x (lambda)And (5) extinguishing. Observing the noise floor of the measured spectrum data x (lambda), obtaining gradient data Dx (lambda) by solving the gradient of the measured spectrum data which is 20dB higher than the noise floor, and searching the data points of which the signs of the data points at two adjacent sides in the Dx (lambda) are changed from positive to negative, wherein the corresponding lambda is taken as the peak position lambda of the ith spectrum peak i (i=1, …, M) pieces of peak position information are obtained in total. Due to the modulation frequency f in the present embodiment m Setting to 4GHz, the modulation spectrum is too close, and only 2 spectral peaks and corresponding peak positions lambda are identified by the method i (i=1, 2), so that an additional addition of 3 spectral peaks and their corresponding peak positions λ is required p (p=3, 4, 5), select λ 2 As a rough peak position value of the newly added spectral peak, i.e. lambda p (p＝3,4,5)＝λ 2 . Thus, new peak position information lambda is obtained i (i＝1,…,5)。
Peak position lambda for each spectral peak i Applying a deviation Deltalambda i (i=1, …, 5) to obtain a new peak position λ of the spectral peak i +Δλ i The method comprises the steps of carrying out a first treatment on the surface of the Constructing an estimate of the measured spectrum x (λ):
wherein a is i For peak position lambda of spectral line i +Δλ i Amplitude value of delta [ lambda- (lambda) i +Δλ i )]Is a dirac function for λ.
By means of an optimization algorithm combined with least squares fitting
(wherein a= (a) 1 ,…,a 5 )，ΔΛ＝(Δλ 1 ,…,Δλ 5 ) N is the number of points of the spectrum data) minimum is an objective function to obtain peak position lambda of each spectrum peak i +Δλ i And the corresponding amplitude value a i . The specific solving steps are as follows:
t1: let ΔΛ= (Δλ) 1 ,…,Δλ 5 ) As a search variable of the genetic algorithm, the dimension is 5, and the search range is defined as (-0.25 nm,0.25 nm);
t2: encoding delta lambda to generate a chromosome;
t3: randomly generating an initial population with a population size of 100 in a search range, wherein chromosomes of each individual in the population correspond to different peak position deviation amounts delta lambda g (g＝1,…,100)；
T4: ΔΛ of the g-th individual g Substitution into
The least squares fitting problem is then solved with the Levenberg-Marquardt Method (L-M Method) to give ΔΛ=ΔΛ g Amplitude value A at the time g Sum of squares of residuals F g And combining-F g As fitness value of the individual;
t5: repeating the step T4 until the fitness value of all individuals in the population is calculated;
t6: recording ΔΛ of the optimal individual (the individual with the largest fitness value) and an amplitude value a obtained by least squares fitting at the ΔΛ;
t7: selecting a better individual 'survived' in the population by adopting a roulette method, and performing crossing and mutation operation on chromosomes of the better individual 'survived' to generate a next generation population;
t8: repeating the steps T4-T7 until the relative change of the continuous 20-generation optimal fitness value is lower than 10 -6 Then, ΔΛ of the optimal individual in the last generation and the amplitude value a obtained by least squares fitting at this ΔΛ are output.
Finally according to the obtained peak position lambda i +Δλ i And amplitude value a i (i=1, …, 5) to obtain a modulation spectrum
Fig. 3 is a comparison of the measured modulation spectrum of the present embodiment, where the wavelength of the optical carrier is 1550nm and the microwave modulation frequency fm is set to 4GHz, and the modulation spectrum recovered by the method of the present invention. It can be seen that the method successfully recovers the sidebands covered by the carrier wave and improves the spectral resolution.
Claims (5)
1. A method for improving the accuracy of modulation spectroscopy measurements, comprising the steps of:
s1: the method comprises the steps of constructing a modulation spectrum testing device, wherein the modulation spectrum testing device comprises a narrow linewidth laser, an electro-optic modulator, a spectrum analysis module, a microwave signal source and a data acquisition and control module, the narrow linewidth laser, the electro-optic modulator and the spectrum analysis module are sequentially and optically connected, the microwave signal source is electrically connected with the electro-optic modulator, and the data acquisition and control module is respectively connected with the microwave signal source and the spectrum analysis module through a data bus; the method comprises the steps that an optical carrier wave output by a narrow linewidth laser device is incident to an electro-optical modulator, an optical signal output by the electro-optical modulator is incident to a spectrum analysis module, a data acquisition and control module is used for setting a microwave signal source to output a microwave signal with specific frequency and power, the microwave signal is loaded to the electro-optical modulator, and spectrum data of the spectrum analysis module are acquired through the data acquisition and control module;
s2: the data acquisition and control module controls the microwave signal source to output microwave signals with specific frequency and power, the electro-optical modulator outputs modulated optical signals at the moment, and the data acquisition and control module acquires the spectrum data x (lambda) of the spectrum analysis module;
s3: the data acquisition and control module controls the microwave signal source to close microwave signal output, at the moment, the electro-optical modulator outputs an idle light signal, and the data acquisition and control module acquires the spectrum data h (lambda) of the spectrum analysis module;
s4: given the number N of spectral peaks in advance, if the peak position lambda of the ith spectral peak is known i (i=1, …, N), steps S5 and S6 are skipped directly to step S7;
s5: observing the noise floor of the measured spectrum data x (lambda), obtaining gradient data Dx (lambda) by solving the gradient of the measured spectrum data which is 20dB higher than the noise floor, and searching the data points of which the signs of the data points at two adjacent sides in the Dx (lambda) are changed from positive to negative, wherein the corresponding lambda is taken as the peak position lambda of the ith spectrum peak i (i=1, …, M) to obtain M pieces of peak position information in total;
s6: if M>Directly enter step S7, otherwise add N-M pieces of peak position information corresponding to peak position lambda N+p The value of (p=1, …, N-M) can be determined from λ i (i=1, …, M) to obtain new peak position information λ i (i＝1,…,N)；
S7: peak position lambda for each spectral peak i Applying a deviation Deltalambda i (i=1, …, N) to obtain a new peak position λ of the spectral peak i +Δλ i The method comprises the steps of carrying out a first treatment on the surface of the Constructing an estimate of the measured spectrum x (λ):
wherein a is i For peak position lambda of spectral line i +Δλ i Amplitude value of delta [ lambda- (lambda) i +Δλ i )]Is a dirac function for λ;
s8: by means of an optimization algorithm combined with least squares fitting
(wherein a= (a) 1 ,…,a N )，ΔΛ＝(Δλ 1 ,…,Δλ N ) N is the number of points of the spectrum data) minimum is an objective function to obtain peak position lambda of each spectrum peak i +Δλ i And the corresponding amplitude value a i ；
S9: peak position lambda obtained by S8 i +Δλ i And amplitude value a i (i=1, …, N) to obtain a modulation spectrum
2. The method according to claim 1, wherein in the step S8, the optimization algorithm is a genetic algorithm, and the specific steps of the genetic algorithm in combination with least squares fitting to calculate the peak position deviation ΔΛ of the spectrum peak and the corresponding amplitude value a are as follows:
t1: let ΔΛ= (Δλ) 1 ,…,Δλ N ) As a search variable of the genetic algorithm, the dimension is N, and a search range is limited according to actual conditions;
t2: encoding delta lambda to generate a chromosome;
t3: randomly generating an initial population with a population size G in a search range, wherein chromosomes of each individual in the population correspond to different peak position deviation amounts delta lambda g (g＝1,…,G)；
T4: ΔΛ of the g-th individual g Substitution into
The least squares fitting problem is then solved with the Levenberg-Marquardt Method (L-M Method) to give ΔΛ=ΔΛ g Amplitude value A at the time g Sum of squares of residuals F g And combining-F g As fitness value of the individual;
t5: repeating the step T4 until the fitness value of all individuals in the population is calculated;
t6: recording the delta lambda of the optimal individual, namely the individual with the largest fitness value, and the amplitude value A obtained by least square fitting under the delta lambda;
t7: selecting a better individual 'survived' in the population by adopting a roulette method, and performing crossing and mutation operation on chromosomes of the better individual 'survived' to generate a next generation population;
t8: and repeating the steps T4-T7 until the relative change of the optimal fitness value is lower than the set value, and then outputting the delta lambda of the optimal individual in the last generation and the amplitude value A obtained by least square fitting under the delta lambda.
3. The method according to claim 1, wherein in step S5, the change from positive to negative is generally made up of more than 2 consecutive positive and more than 2 consecutive negative.
4. The method according to claim 1, wherein in step S7, δ [ λ - (λ) i +Δλ i )]And can also be replaced by a linear function of the microwave signal output by the microwave signal source.
5. The method according to claim 2, wherein in step T8, the optimization is generally performed until the relative change of 20 consecutive optimal fitness values is lower than a set value.
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| CN103852444A (en) * | 2014-03-19 | 2014-06-11 | 中国人民解放军装备学院 | Calibration-free modulation spectrum measuring system |
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