CN109724698A - A kind of wide-band spectrum instrument spectral signal real-time calibration method - Google Patents
A kind of wide-band spectrum instrument spectral signal real-time calibration method Download PDFInfo
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Abstract
The invention proposes a kind of wide-band spectrum instrument spectral signal real-time calibration methods.The measurement data point set for constructing spectral signal, obtains spectral signal maximum point set by peak-seeking algorithm；Wavelength calibration is carried out using the method for the three rank multinomials fitting based on least square；Parameterized treatment is carried out using pixel serial number of the Chord Length Parameterization method to spectrum measuring data point, then B-spline Curve fitting is carried out to the spectrum measuring data point after parameterized treatment, further progress sample interpolation completes the work of light intensity calibration；The corresponding relationship that wavelength and light intensity are established according to Wavelength calibration and light intensity calibration, completes the real-time calibration to spectral signal.Wavelength scaling and light intensity calibration of the present invention suitable for wide-band spectrum instrument calibration process, and there is real-time, practicability and higher accuracy.
Description
Technical field
The present invention relates to spectrometer technical fields, and in particular, to a kind of wide-band spectrum instrument spectral signal real-time calibration
Method.
Background technique
Currently, the spectrometer that infrared band or ultraviolet band etc. are absorbed in a certain wave band measurement can reach compared with high measurement essence
Degree, correlative study are more mature.And the research for the broadband micro spectrometer that measurement range is 200-1100nm is less, and
Majority can only reach the resolution ratio of certain precision in ultraviolet or infrared band, and wide-band spectrum instrument is widely used, and modernizes skill
Requirement of the development of art to the function and performance of spectrometer is improving always, and the market demand also can be increasing.And existing width
There are two main problems for band of light spectrometer, first is that there are restriction relations between spectral region and resolution ratio, it is more difficult to wider
More uniform and higher spectral resolution is obtained in spectral region；Second is that spectral region includes ultraviolet band region, due to CCD
It is not high that the performance of detector will cause the ultraviolet response sensitivity of instrument.And suitable spectroscopic data Processing Algorithm can be effectively improved this
Two problems.
One of an important factor for influencing two problems of spectrometer is exactly the calibration process of spectrum.Spectral calibration is mainly studied
Corresponding relationship between each pixel output spectrum signal of CCD and spectral wavelength to be measured, spectral radiant flux, i.e. wavelength scaling and light intensity
Calibration.The functional relation that pixel serial number Yu spectral wavelength numerical value can be determined using wavelength scaling algorithm obtains the wave of spectrometer
Long calibration equation；Light intensity calibration refers to the fitting to different-waveband light intensity.Thus the applicability of spectral calibration algorithm is in very great Cheng
The accuracy of final spectrogram can be determined on degree.
The available smooth accurate spectrogram of spectral calibration, and improve the confidence level of spectral instrument.The master of spectral calibration
Wanting task is determining spectral wavelength position and spectrum stability, and tuning wavelength deviates, and measures spectral response functions.CCD detection
Device output and the one-to-one response signal of pixel serial number, show measurement data by PC machine software systems, are saved simultaneously
It handles standard spectrum and calibrates output data.Current main calibrating method has monochromator method and standard spectral method etc., monochromator
Method continuously exports monochromatic collimated light, and wavelength and the bandwidth calibration of wide spectral range can be achieved at the same time；Standard spectral method utilizes sodium
The standard spectrum of lamp or mercury lamp, it can be achieved that high-resolution, linear light spectrometer Wavelength calibration.The calibration of standard spectral method mostly uses
Piecewise fitting, Gauss curve fitting and polynomial fitting.
Light intensity calibration research is relatively fewer.Currently, curve-fitting method has fitting of a polynomial, RBF (Radial Basis
Function curve matching, Bezier curve fitting, B-spline curves fitting and BP neural network fitting) etc..Fitting of a polynomial
Precision is limited, and B-spline curves precision is slightly higher, BP neural network, need to select suitable network structure, realizes complicated.It is more applicable
Also need further to be studied in the selection of the scaling algorithm of spectrum analysis.
It traditional calibrating method or is difficult to find out weak peak position in the spectral line profile of broadband complexity or mention
But speed is sacrificed while high accuracy, it is difficult to meet real-time display.Therefore one kind is needed to can apply to wide-band spectrum instrument
Real-time calibration method.
Summary of the invention
In order to solve above-mentioned technical problem, the object of the present invention is to provide a kind of wide-band spectrum instrument spectral signals
Real-time calibration method, to solve the problems, such as to be difficult to realize accurate real-time calibration in wider spectral region.
The technical scheme adopted by the invention is that a kind of wide-band spectrum instrument spectral signal real-time calibration method, main to walk
Suddenly it is divided into three steps, i.e. peak-seeking algorithm, wavelength scaling and light intensity calibration.Specific steps are as follows:
Step 1: constructing the measurement data point set of spectral signal, spectral signal maximum point set is obtained by peak-seeking algorithm
It closes；
Step 2: Wavelength calibration is carried out using the method for the three rank multinomials fitting based on least square；
Step 3: parameterized treatment being carried out using pixel serial number of the Chord Length Parameterization method to spectrum measuring data point, then to ginseng
Numberization treated spectrum measuring data point carries out B-spline Curve fitting, and it is fixed that further progress sample interpolation completes light intensity
Target work；
Step 4: establishing the corresponding relationship of wavelength and light intensity according to Wavelength calibration and light intensity calibration, complete to spectral signal
Real-time calibration；
Preferably, constructing the measurement data point set of spectral signal described in step 1 are as follows:
Spectral signal is acquired by wide-band spectrum instrument, by CCD camera acquisition in wide-band spectrum instrument to construct light
The measurement data point set of spectrum signal:
U={ (x0,z0),(x1,z1),...,(xN,zN)}
Wherein, (xi,zi), i=0,1 ..., N are the measurement data points of i-th of spectral signal, and N is the measurement of spectral signal
The measurement data quantity of spectral signal, x in set of data pointsiIndicate the pixel serial number of i-th of spectrum measuring data point, ziIt indicates
The light intensity of i-th of spectrum measuring data point；
Spectral signal maximum point set is obtained by peak-seeking algorithm described in step 1 are as follows:
According to peak-seeking algorithm, by traversing the measurement data point set U of spectral signal, sequence successively compares zi-1, zi,
zi+1Size, if meeting zi-1< ziAnd zi> zi+1As maximum point obtains spectral signal maximum point set i.e. spectral line peak
It is worth position are as follows:
Wherein,For KjThe measurement data points of a spectral signal i.e. j-th of spectral signal
Maximum point, M are the quantity of spectral signal maximum point in spectral signal maximum point set,Indicate KjA spectrum is surveyed
The pixel serial number of i.e. j-th spectral signal maximum point of pixel serial number of data point is measured,Indicate KjA spectrum measuring data
The light intensity of the i.e. j-th spectral signal maximum point of light intensity of point.
Preferably, carrying out wavelength mark using the method for the three rank multinomials fitting based on least square described in step 2
It is set to:
Spectrometer measurement wave band is y ∈ [y1,y2], M characteristic spectral line of the Calibrating source in same wave band
On the basis of；
Indicate the pixel serial number of j-th of spectral signal maximum point,Indicate j-th of spectral signal maximum point
The corresponding wavelength of pixel serial number, if matched curve is WithCorresponding polynomial equation are as follows:
Wherein, M is the quantity of spectral signal maximum point in spectral signal maximum point set, a0For three rank multinomials
First coefficient, a1For the second coefficient of three rank multinomials, a2For the third coefficient of three rank multinomials, a3It is the of three rank multinomials
Four coefficients；
It is handled using least square rule, pointThe deviation at place are as follows:
Least square rule is exactly to minimize sum of square of deviationsI.e.
To makeMinimum, respectively to independent variable a0、a1、a2、a3Local derviation is sought, enabling its value is 0；
By the wavelength of M characteristic spectral line of Calibrating sourceWith corresponding spectral signal maximum point
Pixel serial numberAbove-mentioned formula is substituted into, the coefficient solution that can obtain least square equations is solved
Finally acquire the fitting formula of pixel serial number and wavelength are as follows:
Obtain the corresponding relationship formula of continuous pixel serial number and wavelength are as follows:
Wherein x ∈ [x0,xN] it is continuous pixel serial number, y ∈ [y1,y2] it is spectrometer measurement wave band；
According to the corresponding relationship of step 1 and step 2 available pixel serial number and wavelength, wavelength scaling work is completed.
Preferably, carrying out parameter using pixel serial number of the Chord Length Parameterization method to spectrum measuring data point described in step 3
Change processing:
To the pixel serial number x of N+1 spectrum measuring data pointi, i=0,1 ..., N carries out Chord Length Parameterization processing:
Wherein, xi-xi-1For string side vector, tiFor xiRespective value after parametrization；
Always chord length is
B-spline Curve fitting is carried out to the spectrum measuring data point after parameterized treatment described in step 3:
Establish B-spline Curve model are as follows:
Wherein, q=0,1 ..., M*, M*≤ N is interstitial content, PqFor control node, Nq,3It (t) is 3 specification B-splines
Basic function is derived according to recurrence formula method:
Control node Pq, q=1,2 ..., M*- 1 composition node matrix equation Matrix_P, by equilibrium relationships reverse node matrix equation
Matrix_P has:
(Matrix_NTMatrix_N) Matrix_P=Matrix_R
Wherein, i=1,2 ..., N-1, matrix Matrix_R are control node PqVector data matrix, RvFor light intensity zv
Vector data difference；
Calculate control node Pq, q=1,2 ..., M*- 1 value, by B-spline Curve model, i.e. z0=B (0), zN
=B (1), can obtain P0、Value, therefore the specific function expression of the cubic B-spline of matched curve B (t) can be obtained；
Further progress sample interpolation described in step 3 completes the work of light intensity calibration:
Suitable hits H (H > > N) is chosen as needed to sample B-spline Curve, an available system
The discrete data point of columnHave:
Wherein L=1/H-1 chooses a series of discrete data point for the sampling interval in order to obtain continuous light intensity dataAs the benchmark of light intensity fitting, have:
Wherein, L'=x N-x0/ H-1 is continuous pixel serial number x, x ∈ (x0,xN) value interval, sequential connection discrete data
Point Dj*, j*=0,1 ..., H-1, so that it may obtain continuous light intensity data z, have:
To complete light intensity calibration work.
Preferably, establishing the corresponding relationship of wavelength and light intensity described in step 4 are as follows:
It demarcates to obtain the corresponding wavelength of continuous pixel serial number x to be y according to step 2 medium wavelength, be demarcated according to light intensity in step 3
Obtaining the corresponding light intensity of continuous pixel serial number x is z, and obtaining the corresponding light intensity of wavelength y is z, it may be assumed that
(y,z),y∈[y1,y2]
To complete the real-time calibration of spectral signal.
The invention has the following advantages that
A kind of wide-band spectrum instrument spectral signal real-time calibration method of the present invention, acquires spectral line peak value position using peak-seeking algorithm
It sets, calculating speed can satisfy the needs of real-time display and can also have preferable precision；Wavelength scaling is used based on minimum two
Three rank multinomials of multiplication are fitted, and are once accurately calibrated using the progress of known illuminant characterization spectral line, scaling light source is special
Sign spectral line number is more and distribution is more uniform, then the calibration results are more accurate；Light intensity calibration is fitted using B-spline Curve, not only
Have the advantages that Bezier method also overcomes the defect of Bezier curve matched curve inaccuracy in complex curve, three
Secondary B-spline fitting can preferably reflect the tendency of curve entirety, and fitting result is more smooth, and have relatively better part quasi-
Effect is closed, the light intensity calibration of spectrum discrete signal is suitble to.
Detailed description of the invention
Fig. 1: for peak-seeking algorithm flow chart；
Fig. 2: for wavelength scaling flow chart；
Fig. 3: flow chart is calibrated for light intensity；
Fig. 4: for the three rank multinomial matched curve of low pressure mercury lamp least square；
Fig. 5: for the wavelength scaling evaluation index of three rank multinomial of least square fitting；
Fig. 6: to carry out the selected data of B-spline Curve fitting experiment；
Fig. 7: when for hits being 15 Fig. 6 data are carried out with the result of B-spline Curve fitting；
Fig. 8: when for hits being 1000 Fig. 6 data are carried out with the result of B-spline Curve fitting；
Fig. 9: for the result for carrying out B-spline Curve fitting to deuterium lamp spectral signal；
Figure 10: to amplify part (spectral band 590-600nm) spectrogram to Fig. 9；
Figure 11: for the result for carrying out multinomial (20 rank) fitting to deuterium lamp spectral signal；
Figure 12: the method for the present invention flow chart.
Specific embodiment
Understand for the ease of those of ordinary skill in the art and implement the present invention, with reference to the accompanying drawings and embodiments to this hair
It is bright to be described in further detail, it should be understood that implementation example described herein is merely to illustrate and explain the present invention, not
For limiting the present invention.
Embodiments of the present invention are introduced below with reference to Fig. 1 to Figure 12, specifically:
Step 1: constructing the measurement data point set of spectral signal, spectral signal maximum point set is obtained by peak-seeking algorithm
It closes；
The measurement data point set of spectral signal is constructed described in step 1 are as follows:
Spectral signal is acquired by wide-band spectrum instrument, by CCD camera acquisition in wide-band spectrum instrument to construct light
The measurement data point set of spectrum signal:
U={ (x0,z0),(x1,z1),...,(xN,zN)}
Wherein, (xi,zi), i=0,1 ..., N are the measurement data points of i-th of spectral signal, and N is the measurement of spectral signal
The measurement data quantity of spectral signal, x in set of data pointsiIndicate the pixel serial number of i-th of spectrum measuring data point, ziIt indicates
The light intensity of i-th of spectrum measuring data point；
Spectral signal maximum point set is obtained by peak-seeking algorithm described in step 1 are as follows:
According to peak-seeking algorithm, by traversing the measurement data point set U of spectral signal, sequence successively compares zi-1, zi,
zi+1Size, if meeting zi-1< ziAnd zi> zi+1As maximum point obtains spectral signal maximum point set i.e. spectral line peak
It is worth position are as follows:
Wherein,For KjThe measurement data points of a spectral signal i.e. j-th of spectral signal
Maximum point, M are the quantity of spectral signal maximum point in spectral signal maximum point set,Indicate KjA spectrum is surveyed
The pixel serial number of i.e. j-th spectral signal maximum point of pixel serial number of data point is measured,Indicate KjA spectrum measuring data
The light intensity of the i.e. j-th spectral signal maximum point of light intensity of point.
Step 2: Wavelength calibration is carried out using the method for the three rank multinomials fitting based on least square；
Wavelength calibration is carried out using the method for the three rank multinomials fitting based on least square described in step 2 are as follows:
Spectrometer measurement wave band is y ∈ [y1,y2], M characteristic spectral line of the Calibrating source in same wave bandOn the basis of；
Indicate the pixel serial number of j-th of spectral signal maximum point,Indicate j-th of spectral signal maximum point
The corresponding wavelength of pixel serial number, if matched curve is WithCorresponding polynomial equation are as follows:
Wherein, M is the quantity of spectral signal maximum point in spectral signal maximum point set, a0For three rank multinomials
First coefficient, a1For the second coefficient of three rank multinomials, a2For the third coefficient of three rank multinomials, a3It is the of three rank multinomials
Four coefficients；
It is handled using least square rule, pointThe deviation at place are as follows:
Least square rule is exactly to minimize sum of square of deviationsI.e.
To makeMinimum, respectively to independent variable a0、a1、a2、a3Local derviation is sought, enabling its value is 0；
By the wavelength of M characteristic spectral line of Calibrating sourceWith corresponding spectral signal maximum point
Pixel serial numberAbove-mentioned formula is substituted into, the coefficient solution that can obtain least square equations is solved
Finally acquire the fitting formula of pixel serial number and wavelength are as follows:
Obtain the corresponding relationship formula of continuous pixel serial number and wavelength are as follows:
Wherein x ∈ [x0,xN] it is continuous pixel serial number, y ∈ [y1,y2] it is spectrometer measurement wave band；
According to the corresponding relationship of step 1 and step 2 available pixel serial number and wavelength, wavelength scaling work is completed.
Step 3: parameterized treatment being carried out using pixel serial number of the Chord Length Parameterization method to spectrum measuring data point, then to ginseng
Numberization treated spectrum measuring data point carries out B-spline Curve fitting, and it is fixed that further progress sample interpolation completes light intensity
Target work；
Parameterized treatment is carried out using pixel serial number of the Chord Length Parameterization method to spectrum measuring data point described in step 3:
To the pixel serial number x of N+1 spectrum measuring data pointi, i=0,1 ..., N carries out Chord Length Parameterization processing:
Wherein, xi-xi-1For string side vector, tiFor xiRespective value after parametrization；
Always chord length is
B-spline Curve fitting is carried out to the spectrum measuring data point after parameterized treatment described in step 3:
Establish B-spline Curve model are as follows:
Wherein, q=0,1 ..., M*, M*≤ N is interstitial content, PqFor control node, Nq,3It (t) is 3 specification B-splines
Basic function is derived according to recurrence formula method:
Control node Pq, q=1,2 ..., M*- 1 composition node matrix equation Matrix_P, by equilibrium relationships reverse node matrix equation
Matrix_P has:
(Matrix_NTMatrix_N) Matrix_P=Matrix_R
Wherein, i=1,2 ..., N-1, matrix Matrix_R are control node PqVector data matrix, RvFor light intensity zv
Vector data difference；
Calculate control node Pq, q=1,2 ..., M*- 1 value, by B-spline Curve model, i.e. z0=B (0), zN
=B (1), can obtain P0、PM*Value, therefore the specific function expression of the cubic B-spline of matched curve B (t) can be obtained；
Further progress sample interpolation described in step 3 completes the work of light intensity calibration:
Suitable hits H (H > > N) is chosen as needed to sample B-spline Curve, an available system
The discrete data point of columnHave:
Wherein L=1/H-1 chooses a series of discrete data point for the sampling interval in order to obtain continuous light intensity dataAs the benchmark of light intensity fitting, have:
Wherein, L'=xN-x0/H-1For continuous pixel serial number x, x ∈ (x0,xN) value interval, sequential connection discrete data
PointContinuous light intensity data z can be obtained, is had:
To complete light intensity calibration work.
Step 4: establishing the corresponding relationship of wavelength and light intensity according to Wavelength calibration and light intensity calibration, complete to spectral signal
Real-time calibration；
The corresponding relationship of wavelength and light intensity is established described in step 4 are as follows:
It demarcates to obtain the corresponding wavelength of continuous pixel serial number x to be y according to step 2 medium wavelength, be demarcated according to light intensity in step 3
Obtaining the corresponding light intensity of continuous pixel serial number x is z, and obtaining the corresponding light intensity of wavelength y is z, it may be assumed that
(y,z),y∈[y1,y2]
To complete the real-time calibration of spectral signal.
Spectral signal, spectrometer measurement wave band y ∈ are acquired with the ccd sensor (2048 pixels) of model ILX554B
(200nm, 1100nm) does further specific description to technical solution of the present invention.
Fig. 1 is peak-seeking algorithm flow chart, constructs the measurement data point set of spectral signal, obtains spectrum by peak-seeking algorithm
Signal maximum point set.
Fig. 2 is wavelength scaling flow chart, is fitted using three rank multinomials based on least square, determines pixel serial number and wave
Long function corresponding relationship.
Fig. 3 is that light intensity calibrates flow chart, is joined using pixel serial number of the Chord Length Parameterization method to spectrum measuring data point
Numberization processing, then B-spline Curve fitting, further progress sampling are carried out to the spectrum measuring data point after parameterized treatment
Interpolation completes the work of light intensity calibration.
Fig. 4 is the three rank multinomial matched curve of low pressure mercury lamp least square.Select 6 characteristic spectral lines of low pressure mercury lamp:
253.65nm, 365.01nm, 404.66nm, 435.84nm, 546.07nm, 576.96nm export CCD detector undetermined
Mark spectrogram obtains the pixel serial number at 6 peak values using peak-seeking algorithm: 121,357,441,508,745,813, pass through substitution
Equation after the fitting of three ranks, finally obtains fitting result.As can be seen from Figure 4 fitting effect is splendid, and can satisfy needs
It asks.
Fig. 5 is the wavelength scaling evaluation index of three rank multinomial of least square fitting.Each fitting wavelength of three rank multinomials
Residual sum of square be 0.049638, standard error 0.111398, value all very little can substantially meet required precision.Correlation refers to
Number size is 0.999999, and nearly close to 1, fitting degree is relatively good, and compares these and refer to target value, and three ranks are substantially better than
Single order and second order polynomial fit.
Fig. 6 is to carry out the selected data of B-spline Curve fitting experiment.Fig. 7 is hits when being 15 to Fig. 6 data
Carry out B-spline Curve fitting as a result, Fig. 8, which is hits, carries out B-spline Curve fitting to Fig. 6 data when being 1000
Result.When hits is 15, B-spline Curve fitting result is as shown in Figure 7.When hits is 1000, fitting knot
Fruit is as shown in Figure 8.By Fig. 7 and Fig. 8 it is found that B-spline Curve can advantageously ensure that in this way measurement by each measurement point
The accuracy of data, and change the slickness of matched curve by controlling hits.
Fig. 9 is to the progress B-spline Curve fitting of deuterium lamp spectral signal as a result, Figure 10 is to amplify part (light to Fig. 9
Compose wave band 590-600nm) spectrogram.It is computed, the fitting index of correlation is 0.9997, and it is preferably smooth to indicate that matched curve has
Property.It follows that B-spline curve can preferably reflect the tendency of curve entirety, fitting result is more smooth, and have than
More good local fit effect is suitble to the light intensity fitting of spectrum discrete signal.
Figure 11 be deuterium lamp spectral signal has been carried out multinomial (20 rank) fitting as a result, as can be seen from the results, multinomial
Fitting is realized simply, but precision is limited, is not suitable for None-linear approximation and the unordered data containing singular value, that is, is not suitable for width
The light intensity of wave band miniature spectrometer is calibrated.Thus, B-spline Curve is more suitable for the calibration of broadband micro spectrometer light intensity
Algorithm.
Pass through comparative experiments, it was demonstrated that a kind of wide-band spectrum instrument spectral signal real-time calibration method of the present invention is suitable for wide wave
Wavelength scaling and light intensity calibration in section spectrometer calibration process, and there is real-time, practicability and higher accuracy.
It should be understood that the above-mentioned description for preferred embodiment is more detailed, can not therefore be considered to this
The limitation of invention patent protection range, those skilled in the art under the inspiration of the present invention, are not departing from power of the present invention
Benefit requires to make replacement or deformation under protected ambit, fall within the scope of protection of the present invention, this hair
It is bright range is claimed to be determined by the appended claims.
Claims (5)
1. a kind of wide-band spectrum instrument spectral signal real-time calibration method characterized by comprising
Step 1: constructing the measurement data point set of spectral signal, spectral signal maximum point set is obtained by peak-seeking algorithm；
Step 2: Wavelength calibration is carried out using the method for the three rank multinomials fitting based on least square；
Step 3: parameterized treatment being carried out using pixel serial number of the Chord Length Parameterization method to spectrum measuring data point, then to parametrization
Treated, and spectrum measuring data point carries out B-spline Curve fitting, and further progress sample interpolation completes light intensity calibration
Work；
Step 4: establishing the corresponding relationship of wavelength and light intensity according to Wavelength calibration and light intensity calibration, complete the reality to spectral signal
Shi Dingbiao.
2. wide-band spectrum instrument spectral signal real-time calibration method according to claim 1, it is characterised in that: in step 1
The measurement data point set of the building spectral signal are as follows:
Spectral signal is acquired by wide-band spectrum instrument, by CCD camera acquisition in wide-band spectrum instrument to construct spectrum letter
Number measurement data point set:
U={ (x0,z0),(x1,z1),...,(xN,zN)}
Wherein, (xi,zi), i=0,1 ..., N are the measurement data points of i-th of spectral signal, and N is the measurement data of spectral signal
The measurement data quantity of spectral signal, x in point setiIndicate the pixel serial number of i-th of spectrum measuring data point, ziIt indicates i-th
The light intensity of spectrum measuring data point；
Spectral signal maximum point set is obtained by peak-seeking algorithm described in step 1 are as follows:
According to peak-seeking algorithm, by traversing the measurement data point set U of spectral signal, sequence successively compares zi-1,zi,zi+1It is big
It is small, if meeting zi-1< ziAnd zi> zi+1As maximum point obtains spectral signal maximum point set i.e. spectral line peak position
Are as follows:
Wherein,For KjThe measurement data points of a spectral signal i.e. j-th of spectral signal maximum
Point, M are the quantity of spectral signal maximum point in spectral signal maximum point set,Indicate KjA spectrum measuring data
The pixel serial number of i.e. j-th spectral signal maximum point of pixel serial number of point,Indicate KjThe light of a spectrum measuring data point
It is by force the light intensity of j-th of spectral signal maximum point.
3. wide-band spectrum instrument spectral signal real-time calibration method according to claim 1, it is characterised in that: in step 2
The method using the three rank multinomials fitting based on least square carries out Wavelength calibration are as follows:
Spectrometer measurement wave band is y ∈ [y1,y2], M characteristic spectral line of the Calibrating source in same wave band
On the basis of；
Indicate the pixel serial number of j-th of spectral signal maximum point,Indicate the pixel of j-th of spectral signal maximum point
The corresponding wavelength of serial number, if matched curve is WithCorresponding polynomial equation are as follows:
Wherein, M is the quantity of spectral signal maximum point in spectral signal maximum point set, a0It is the first of three rank multinomials
Coefficient, a1For the second coefficient of three rank multinomials, a2For the third coefficient of three rank multinomials, a3For the 4th system of three rank multinomials
Number；
It is handled using least square rule, pointThe deviation at place are as follows:
Least square rule is exactly to minimize sum of square of deviationsI.e.
To makeMinimum, respectively to independent variable a0、a1、a2、a3Local derviation is sought, enabling its value is 0；
By the wavelength of M characteristic spectral line of Calibrating sourceWith the pixel of corresponding spectral signal maximum point
Serial numberAbove-mentioned formula is substituted into, the coefficient solution that can obtain least square equations is solved
Finally acquire the fitting formula of pixel serial number and wavelength are as follows:
Obtain the corresponding relationship formula of continuous pixel serial number and wavelength are as follows:
Wherein x ∈ [x0,xN] it is continuous pixel serial number, y ∈ [y1,y2] it is spectrometer measurement wave band；
According to the corresponding relationship of step 1 and step 2 available pixel serial number and wavelength, wavelength scaling work is completed.
4. wide-band spectrum instrument spectral signal real-time calibration method according to claim 1, it is characterised in that: step 3 institute
It states and parameterized treatment is carried out using pixel serial number of the Chord Length Parameterization method to spectrum measuring data point:
To the pixel serial number x of N+1 spectrum measuring data pointi, i=0,1 ..., N carries out Chord Length Parameterization processing:
Wherein, xi-xi-1For string side vector, tiFor xiRespective value after parametrization；
Always chord length is
B-spline Curve fitting is carried out to the spectrum measuring data point after parameterized treatment described in step 3:
Establish B-spline Curve model are as follows:
Wherein, q=0,1 ..., M*, M*≤ N is interstitial content, PqFor control node, Nq,3It (t) is 3 specification B-spline base letters
Number is derived according to recurrence formula method:
Control node Pq, q=1,2 ..., M*- 1 composition node matrix equation Matrix_P, by equilibrium relationships reverse node matrix equation
Matrix_P has:
(Matrix_NTMatrix_N) Matrix_P=Matrix_R
Wherein, i=1,2 ..., N-1, matrix Matrix_R are control node PqVector data matrix, RvFor light intensity zvArrow
Measure data difference；
Calculate control node Pq, q=1,2 ..., M*- 1 value, by B-spline Curve model, i.e. z0=B (0), zN=B (1),
P can be obtained0、Value, therefore the specific function expression of the cubic B-spline of matched curve B (t) can be obtained；
Further progress sample interpolation described in step 3 completes the work of light intensity calibration:
Suitable hits H (H > > N) is chosen as needed to sample B-spline Curve, it is available a series of
Discrete data pointHave:
Wherein L=1/H-1 chooses a series of discrete data point for the sampling interval in order to obtain continuous light intensity dataAs the benchmark of light intensity fitting, have:
Wherein, L'=xN-x0/ H-1 is continuous pixel serial number x, x ∈ (x0,xN) value interval, sequential connection discrete data pointContinuous light intensity data z can be obtained, is had:
To complete light intensity calibration work.
5. wide-band spectrum instrument spectral signal real-time calibration method according to claim 1, it is characterised in that: in step 4
The corresponding relationship for establishing wavelength and light intensity are as follows:
It demarcates to obtain the corresponding wavelength of continuous pixel serial number x to be y according to step 2 medium wavelength, demarcates to obtain according to light intensity in step 3
Continuously the corresponding light intensity of pixel serial number x is z, and obtaining the corresponding light intensity of wavelength y is z, it may be assumed that
(y,z),y∈[y1,y2]
To complete the real-time calibration of spectral signal.
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| CN112986161A (en) * | 2021-05-11 | 2021-06-18 | 南京智谱科技有限公司 | Online wavelength calibration method and device for water quality monitoring spectrometer |
| CN113654457A (en) * | 2021-07-22 | 2021-11-16 | 太原理工大学 | Spectrum confocal measuring head wavelength and displacement mapping relation calibration device and fitting method |
| CN113984208A (en) * | 2021-10-26 | 2022-01-28 | 重庆川仪自动化股份有限公司 | Spectrometer wavelength calibration method, system, medium and electronic terminal |
| CN116448739A (en) * | 2023-03-21 | 2023-07-18 | 华北电力大学 | Method for measuring gas phase alkali metal concentration in furnace based on flame self-emission spectrum |
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| CN110487404A (en) * | 2019-09-25 | 2019-11-22 | 台州市维谱智能科技有限公司 | A method of eliminating grating spectrograph Advanced Diffraction influences |
| CN111721734A (en) * | 2020-06-29 | 2020-09-29 | 中国科学院合肥物质科学研究院 | On-orbit spectrum calibration method for infrared very high spectral resolution detector for high-resolution five-number satellite |
| CN112986161A (en) * | 2021-05-11 | 2021-06-18 | 南京智谱科技有限公司 | Online wavelength calibration method and device for water quality monitoring spectrometer |
| CN113654457A (en) * | 2021-07-22 | 2021-11-16 | 太原理工大学 | Spectrum confocal measuring head wavelength and displacement mapping relation calibration device and fitting method |
| CN113984208A (en) * | 2021-10-26 | 2022-01-28 | 重庆川仪自动化股份有限公司 | Spectrometer wavelength calibration method, system, medium and electronic terminal |
| CN113984208B (en) * | 2021-10-26 | 2024-05-31 | 重庆川仪自动化股份有限公司 | Spectrometer wavelength calibration method, spectrometer wavelength calibration system, spectrometer wavelength calibration medium and electronic terminal |
| CN116448739A (en) * | 2023-03-21 | 2023-07-18 | 华北电力大学 | Method for measuring gas phase alkali metal concentration in furnace based on flame self-emission spectrum |
| CN118129905A (en) * | 2024-05-08 | 2024-06-04 | 武汉大学 | Curve type radiation calibration method and system for satellite-borne hyperspectral imager |
| CN118129905B (en) * | 2024-05-08 | 2024-07-02 | 武汉大学 | Curve type radiation calibration method and system for satellite-borne hyperspectral imager |
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