CN109724698B - Real-time calibration method for spectral signals of broadband spectrometer - Google Patents
Real-time calibration method for spectral signals of broadband spectrometer Download PDFInfo
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Abstract
The invention provides a real-time calibration method for a spectrum signal of a broadband spectrometer. Constructing a measurement data point set of the spectral signal, and obtaining a maximum value point set of the spectral signal through a peak searching algorithm; carrying out wavelength calibration by adopting a method of third-order polynomial fitting based on least square; carrying out parameterization on the pixel serial number of the spectral measurement data point by adopting a chord length parameterization method, then carrying out cubic B-spline curve fitting on the parameterized spectral measurement data point, and further carrying out sampling interpolation to finish the work of light intensity calibration; and establishing a corresponding relation between the wavelength and the light intensity according to the wavelength calibration and the light intensity calibration to finish the real-time calibration of the spectrum signal. The invention is suitable for wavelength calibration and light intensity calibration in the calibration process of the broadband spectrometer, and has real-time performance, practicability and higher accuracy.
Description
Technical Field
The invention relates to the technical field of spectrometers, in particular to a real-time calibration method for spectral signals of a broadband spectrometer.
Background
At present, a spectrometer for measuring infrared bands or ultraviolet bands and the like by focusing on a certain band can achieve higher measurement precision, and related research is mature. The research on the broadband micro spectrometer with the measurement range of 200-1100nm is less, most of the broadband micro spectrometers can only achieve resolution with certain precision in ultraviolet or infrared bands, the broadband spectrometers are widely applied, the requirements on the functions and the performances of the spectrometers are always improved due to the development of the modern technology, and the market requirements are increased. The existing broadband spectrometer has two main problems, namely, the spectral range and the resolution ratio have a limiting relationship, so that the uniform and high spectral resolution ratio is difficult to obtain in a wide spectral range; secondly, the spectrum range comprises an ultraviolet band region, and the ultraviolet response sensitivity of the instrument is not high due to the performance of the CCD detector. And a suitable spectral data processing algorithm can effectively improve the two problems.
One of the important factors affecting two problems of spectrometers is the calibration process of the spectra. The spectral calibration is mainly used for researching the corresponding relation between the spectral signal output by each pixel of the CCD and the spectral wavelength and spectral radiant flux to be measured, namely wavelength calibration and light intensity calibration. The functional relation between the pixel serial number and the spectrum wavelength value can be determined by adopting a wavelength calibration algorithm to obtain a wavelength calibration equation of the spectrometer; light intensity scaling refers to fitting light intensities of different wavebands. The applicability of the spectral scaling algorithm will largely determine the accuracy of the final spectrogram.
The spectrum calibration can obtain a smooth and accurate spectrogram and improve the reliability of the spectrometer. The main tasks of spectral calibration are to determine spectral wavelength position and spectral stability, correct wavelength shifts, and determine spectral response functions. The CCD detector outputs response signals corresponding to the pixel serial numbers one by one, and the measured data is displayed, stored and processed by a PC software system to output standard spectrum calibration data. The current main calibration methods comprise a monochrometer method, a standard spectral line method and the like, wherein the monochrometer method continuously outputs monochromatic collimated light and can simultaneously realize wavelength and bandwidth calibration in a wide spectral range; the standard spectral line method can realize the wavelength calibration of a high-resolution linear spectrometer by using a standard spectral line diagram of a sodium lamp or a mercury lamp. The standard spectral line method calibration mostly adopts the algorithms of piecewise fitting, Gaussian fitting and polynomial fitting.
Light intensity scaling studies are relatively rare. At present, the curve fitting method includes polynomial fitting, rbf (radial basis function) curve fitting, Bezier curve fitting, B-spline curve fitting, BP neural network fitting, and the like. The polynomial fitting precision is limited, the B spline curve precision is slightly high, and a BP neural network needs to select a proper network structure, so that the realization is complex. The selection of a calibration algorithm more suitable for spectral analysis is yet to be further investigated.
The traditional calibration method is difficult to find the weak peak position in the broadband complicated spectral line distribution diagram, or the accuracy is improved while the speed is sacrificed, so that the real-time display is difficult to meet. There is therefore a need for a method that can be applied to real-time calibration of broadband spectrometers.
Disclosure of Invention
In order to solve the above technical problems, the present invention provides a real-time calibration method for a spectrum signal of a broadband spectrometer, so as to solve the problem that accurate real-time calibration is difficult to achieve in a wide spectrum range.
The invention adopts the technical scheme that the real-time calibration method for the spectrum signal of the broadband spectrometer mainly comprises three steps, namely peak searching algorithm, wavelength calibration and light intensity calibration. The specific operation steps are as follows:
step 1: constructing a measurement data point set of the spectral signal, and obtaining a maximum value point set of the spectral signal through a peak searching algorithm;
step 2: carrying out wavelength calibration by adopting a method of third-order polynomial fitting based on least square;
and step 3: carrying out parameterization on the pixel serial number of the spectral measurement data point by adopting a chord length parameterization method, then carrying out cubic B-spline curve fitting on the parameterized spectral measurement data point, and further carrying out sampling interpolation to finish the work of light intensity calibration;
and 4, step 4: establishing a corresponding relation between the wavelength and the light intensity according to the wavelength calibration and the light intensity calibration to finish the real-time calibration of the spectrum signal;
preferably, the set of measured data points for constructing the spectrum signal in step 1 is:
collecting the spectrum signal by a broadband spectrometer, and collecting by a CCD camera in the broadband spectrometer to construct a measurement data point set of the spectrum signal:
U＝{(x0,z0),(x1,z1),...,(xN,zN)}
wherein (x)i,zi) N is the measurement data point of the ith spectral signal, N is the measurement data number of the spectral signal in the measurement data point set of the spectral signal, xiNumber of pixels, z, representing the ith spectral measurement data pointiThe light intensity of the ith spectral measurement data point is represented;
in the step 1, the maximum point set of the spectrum signal obtained by the peak searching algorithm is as follows:
according to a peak finding algorithm, by traversing a set of measured data points of a spectral signalSynthesis of U, sequential comparison of zi-1,zi,zi+1If z is satisfiedi-1＜ziAnd z isi＞zi+1Namely, the maximum point, the obtained spectrum signal maximum point set, namely the peak position of the spectral line is as follows:
wherein the content of the first and second substances,
is the K thjThe measurement data point of each spectral signal is the jth spectral signal maximum, M is the number of spectral signal maximum in the set of spectral signal maximum,
denotes the K thjThe pixel serial number of the spectral measurement data point is the pixel serial number of the jth spectral signal maximum value point,
denotes the K thjThe light intensity of the jth spectral signal maximum value point is the light intensity of the spectral measurement data point.
Preferably, the method of step 2 using least-squares-based third-order polynomial fitting is used for wavelength calibration as follows:
the measurement wave band of the spectrometer is y ∈ [ y >1,y2]Calibrating M characteristic spectral lines of light source in same wave band
As a benchmark;
wherein M is the number of the maximum points of the spectrum signal in the maximum point set of the spectrum signal, a0Is the first coefficient of a third-order polynomial, a1A second coefficient of a third-order polynomial, a2A third coefficient of a third order polynomial, a3A fourth coefficient that is a third order polynomial;
processing using least squares, points
The deviation of (a) is:
the least squares rule being to minimize the sum of squares of deviations
Namely, it is
To make it possible to
At minimum, for the independent variable a0、a1、a2、a3Calculating a partial derivative to make the value of the partial derivative be 0;
the wavelengths of M characteristic spectral lines of a calibration light source
And the pixel serial number of the corresponding spectrum signal maximum value point
Substituting the above formula to solve the coefficient solution of least square equation
Finally, the fitting formula of the pixel serial number and the wavelength is obtained as follows:
the corresponding relation between the serial number of the continuous pixel and the wavelength is obtained as follows:
where x ∈ [ x ]0,xN]Is the serial number of the continuous pixel, y belongs to [ y ∈ [)1,y2]Measuring the waveband for a spectrometer;
and (3) according to the step (1) and the step (2), the corresponding relation between the pixel serial number and the wavelength can be obtained, and the wavelength calibration work is completed.
Preferably, the parameterization processing is performed on the pixel sequence numbers of the spectral measurement data points by adopting a chord length parameterization method in the step 3:
pixel serial number x for N +1 spectral measurement data pointsiN, chord length parameterization:
wherein x isi-xi-1Is a chord edge vector, tiIs xiParameterized corresponding values;
total chord length of
Performing cubic B-spline curve fitting on the parameterized spectral measurement data points in step 3:
the cubic B-spline curve model is established as follows:
wherein, q is 0,1*，M*N is less than or equal to the number of nodes, PqTo control the node, Nq,3(t) is a 3-order canonical B-spline basis function, derived according to the recursion formula:
control node Pq,q＝1,2,...,M*-1 forming a node Matrix _ P having the following inverse equation relationship:
(Matrix_NTMatrix_N)Matrix_P＝Matrix_R
where i is 1, 2., N-1, and the Matrix _ R is a control node PqVector data matrix of RvIs the light intensity zvThe vector data difference of (a);
computation control node Pq,
By a cubic B-spline curve model, i.e. z0＝B(0)，zNB (1), can give P0、
Thus, a specific functional expression of a cubic B-spline fitting the curve B (t) can be obtained;
and step 3, further performing sampling interpolation to finish the work of light intensity calibration:
selecting proper sampling number H (H > N) to sample cubic B-spline curve according to requirement to obtain a series of discrete data points
Comprises the following steps:
wherein L1/H-1 is a sampling interval, and a series of discrete data points are selected to obtain continuous light intensity data
As the reference for the light intensity fitting, there are:
wherein the content of the first and second substances,L'＝x N-x0the/H-1 is a serial number x of a continuous pixel, and x belongs to (x)0,xN) Interval of values of (D), connecting discrete data points D in sequencej*J is 0, 1.., H-1, then continuous intensity data z can be obtained, including:
thereby completing the light intensity calibration work.
Preferably, the step 4 of establishing the corresponding relationship between the wavelength and the light intensity is as follows:
obtaining the wavelength y corresponding to the serial number x of the continuous pixel according to the wavelength calibration in the step 2, obtaining the light intensity z corresponding to the serial number x of the continuous pixel according to the light intensity calibration in the step 3, and obtaining the light intensity z corresponding to the wavelength y, namely:
(y,z),y∈[y1,y2]
thereby completing the real-time calibration of the spectrum signal.
The invention has the following advantages:
the invention relates to a real-time calibration method for a broadband spectrometer spectral signal, which adopts a peak searching algorithm to obtain the peak position of a spectral line, and the calculation speed can meet the requirement of real-time display and also has better precision; the wavelength calibration adopts a third-order polynomial based on a least square method for fitting, known light source characteristic spectral lines are utilized for once accurate calibration, and the more the calibration light source characteristic spectral lines are, the more uniform the distribution is, the more accurate the calibration result is; the light intensity calibration adopts cubic B-spline curve fitting, not only has the advantages of the Bezier method, but also overcomes the defect that the curve fitting of the Bezier curve is inaccurate under the condition of a complex curve, the cubic B-spline fitting can better reflect the overall trend of the curve, the fitting result is smoother, and the cubic B-spline curve fitting method has a better local fitting effect and is suitable for the light intensity calibration of the spectrum discrete signal.
Drawings
FIG. 1: a peak-finding algorithm flow chart is obtained;
FIG. 2: a wavelength scaling flow chart;
FIG. 3: calibrating a flow chart for light intensity;
FIG. 4: fitting a curve for a least square third-order polynomial of the low-pressure mercury lamp;
FIG. 5: a wavelength calibration evaluation index for least squares third order polynomial fitting;
FIG. 6: data selected for performing a cubic B-spline curve fitting experiment;
FIG. 7: the result of cubic B-spline curve fitting on the data of FIG. 6 when the sampling number is 15;
FIG. 8: the result of cubic B-spline curve fitting on the data of FIG. 6 when the number of samples is 1000;
FIG. 9: the result is obtained by performing cubic B-spline curve fitting on the deuterium lamp spectrum signal;
FIG. 10: is an enlarged partial (spectrum band 590-600nm) spectrum diagram of FIG. 9;
FIG. 11: is the result of a polynomial (twenty-order) fit to the deuterium lamp spectral signal;
FIG. 12: the method of the invention is a flow chart.
Detailed Description
In order to facilitate the understanding and implementation of the present invention for those of ordinary skill in the art, the present invention is further described in detail with reference to the accompanying drawings and examples, it is to be understood that the embodiments described herein are merely illustrative and explanatory of the present invention and are not restrictive thereof.
The following describes an embodiment of the present invention with reference to fig. 1 to 12, specifically:
step 1: constructing a measurement data point set of the spectral signal, and obtaining a maximum value point set of the spectral signal through a peak searching algorithm;
the measurement data point set of the constructed spectrum signal in the step 1 is as follows:
collecting the spectrum signal by a broadband spectrometer, and collecting by a CCD camera in the broadband spectrometer to construct a measurement data point set of the spectrum signal:
U＝{(x0,z0),(x1,z1),...,(xN,zN)}
wherein (x)i,zi) N is the ith lightMeasurement data points of the spectral signal, N being the number of measurement data points of the spectral signal in the set of measurement data points of the spectral signal, xiNumber of pixels, z, representing the ith spectral measurement data pointiThe light intensity of the ith spectral measurement data point is represented;
in the step 1, the maximum point set of the spectrum signal obtained by the peak searching algorithm is as follows:
according to a peak finding algorithm, z is compared sequentially by traversing a measurement data point set U of the spectrum signali-1,zi,zi+1If z is satisfiedi-1＜ziAnd z isi＞zi+1Namely, the maximum point, the obtained spectrum signal maximum point set, namely the peak position of the spectral line is as follows:
wherein the content of the first and second substances,
is the K thjThe measurement data point of each spectral signal is the jth spectral signal maximum, M is the number of spectral signal maximum in the set of spectral signal maximum,
denotes the K thjThe pixel serial number of the spectral measurement data point is the pixel serial number of the jth spectral signal maximum value point,
denotes the K thjThe light intensity of the jth spectral signal maximum value point is the light intensity of the spectral measurement data point.
Step 2: carrying out wavelength calibration by adopting a method of third-order polynomial fitting based on least square;
and 2, performing wavelength calibration by adopting a least square-based third-order polynomial fitting method as follows:
the measurement wave band of the spectrometer is y ∈ [ y >1,y2]Calibrating M strips of light sources in the same wave bandCharacteristic spectral line
As a benchmark;
wherein M is the number of the maximum points of the spectrum signal in the maximum point set of the spectrum signal, a0Is the first coefficient of a third-order polynomial, a1A second coefficient of a third-order polynomial, a2A third coefficient of a third order polynomial, a3A fourth coefficient that is a third order polynomial;
processing using least squares, points
The deviation of (a) is:
the least squares rule being to minimize the sum of squares of deviations
Namely, it is
To make it possible to
At minimum, for the independent variable a0、a1、a2、a3Calculating a partial derivative to make the value of the partial derivative be 0;
the wavelengths of M characteristic spectral lines of a calibration light source
And the pixel serial number of the corresponding spectrum signal maximum value point
Substituting the above formula to solve the coefficient solution of least square equation
Finally, the fitting formula of the pixel serial number and the wavelength is obtained as follows:
the corresponding relation between the serial number of the continuous pixel and the wavelength is obtained as follows:
where x ∈ [ x ]0,xN]Is the serial number of the continuous pixel, y belongs to [ y ∈ [)1,y2]Measuring the waveband for a spectrometer;
and (3) according to the step (1) and the step (2), the corresponding relation between the pixel serial number and the wavelength can be obtained, and the wavelength calibration work is completed.
And step 3: carrying out parameterization on the pixel serial number of the spectral measurement data point by adopting a chord length parameterization method, then carrying out cubic B-spline curve fitting on the parameterized spectral measurement data point, and further carrying out sampling interpolation to finish the work of light intensity calibration;
and 3, carrying out parameterization treatment on the pixel sequence numbers of the spectral measurement data points by adopting a chord length parameterization method:
pixel serial number x for N +1 spectral measurement data pointsiN, chord length parameterization:
wherein x isi-xi-1Is a chord edge vector, tiIs xiParameterized corresponding values;
total chord length of
Performing cubic B-spline curve fitting on the parameterized spectral measurement data points in step 3:
the cubic B-spline curve model is established as follows:
wherein, q is 0,1*，M*N is less than or equal to the number of nodes, PqTo control the node, Nq,3(t) is a 3-order canonical B-spline basis function, derived according to the recursion formula:
control node Pq,q＝1,2,...,M*-1 forming a node Matrix _ P having the following inverse equation relationship:
(Matrix_NTMatrix_N)Matrix_P＝Matrix_R
where i is 1, 2., N-1, and the Matrix _ R is a control node PqVector data matrix of RvIs the light intensity zvThe vector data difference of (a);
computation control node Pq,q＝1,2,...,M*A value of-1, modeled by a cubic B-spline curve, i.e. z0＝B(0)，zNB (1), can give P0、PM*Thus, a specific functional expression of a cubic B-spline fitting the curve B (t) can be obtained;
and step 3, further performing sampling interpolation to finish the work of light intensity calibration:
selecting proper sampling number H (H > N) to sample cubic B-spline curve according to requirement to obtain a series of discrete data points
Comprises the following steps:
wherein L1/H-1 is a sampling interval, and a series of discrete data points are selected to obtain continuous light intensity data
As the reference for the light intensity fitting, there are:
wherein, L' ═ xN-x0/H-1The serial number x, x belongs to (x) of the continuous image element0,xN) Interval of values of (1), connecting discrete data points in sequence
Continuous intensity data z can be acquired as follows:
thereby completing the light intensity calibration work.
And 4, step 4: establishing a corresponding relation between the wavelength and the light intensity according to the wavelength calibration and the light intensity calibration to finish the real-time calibration of the spectrum signal;
in step 4, the corresponding relationship between the wavelength and the light intensity is established as follows:
obtaining the wavelength y corresponding to the serial number x of the continuous pixel according to the wavelength calibration in the step 2, obtaining the light intensity z corresponding to the serial number x of the continuous pixel according to the light intensity calibration in the step 3, and obtaining the light intensity z corresponding to the wavelength y, namely:
(y,z),y∈[y1,y2]
thereby completing the real-time calibration of the spectrum signal.
The technical scheme of the invention is further specifically explained by using a CCD sensor (2048 pixels) with the model number of ILX554B to collect spectrum signals and a spectrometer to measure a wave band y belonging to the range of 200nm and 1100 nm.
Fig. 1 is a flow chart of a peak finding algorithm, a measurement data point set of a spectrum signal is constructed, and a maximum value point set of the spectrum signal is obtained through the peak finding algorithm.
FIG. 2 is a wavelength calibration flow chart, which determines the functional correspondence between pixel sequence numbers and wavelengths by using least-squares-based third-order polynomial fitting.
FIG. 3 is a light intensity calibration flow chart, wherein a chord length parameterization method is adopted to conduct parameterization on the pixel serial numbers of the spectral measurement data points, then three times of B-spline curve fitting is conducted on the parameterized spectral measurement data points, and further sampling interpolation is conducted to complete the light intensity calibration work.
Fig. 4 is a least squares third-order polynomial fitting curve of the low-pressure mercury lamp. 6 characteristic spectral lines of a low-pressure mercury lamp are selected: 253.65nm, 365.01nm, 404.66nm, 435.84nm, 546.07nm and 576.96nm, and obtaining the pixel sequence numbers of 6 peak values by using a peak searching algorithm on a spectrogram to be marked output by the CCD detector: 121, 357, 441, 508, 745, 813, and finally obtains the fitting result by substituting the equation after the third order fitting. It can be seen from fig. 4 that the fitting effect is excellent and can meet the requirement.
FIG. 5 is a wavelength scaling evaluation index for least squares third order polynomial fitting. The residual sum of squares of each fitting wavelength of the third-order polynomial is 0.049638, the standard error is 0.111398, and the values are all very small and can basically meet the precision requirement. The correlation index is 0.999999, almost approaches to 1, the fitting degree is good, and the third order is obviously superior to the first order and the second order polynomial fitting by comparing the values of the indexes.
FIG. 6 is selected data from a cubic B-spline curve fitting experiment. Fig. 7 shows the results of cubic B-spline curve fitting on the data of fig. 6 when the number of samples is 15, and fig. 8 shows the results of cubic B-spline curve fitting on the data of fig. 6 when the number of samples is 1000. When the number of samples is 15, the result of cubic B-spline curve fitting is shown in fig. 7. When the number of samples is 1000, the fitting result is shown in fig. 8. As can be seen from fig. 7 and 8, the cubic B-spline curve can pass through each measurement point, which is beneficial to ensure the accuracy of the measurement data and change the smoothness of the fitted curve by controlling the sampling number.
Fig. 9 shows the result of cubic B-spline curve fitting on the spectral signal of the deuterium lamp, and fig. 10 shows the enlarged partial (spectral band 590-600nm) spectrum of fig. 9. The fitting correlation index is calculated to be 0.9997, which indicates that the fitting curve has better smoothness. Therefore, cubic B-spline fitting can better reflect the overall trend of the curve, the fitting result is smoother, and the fitting method has a better local fitting effect and is suitable for light intensity fitting of the spectrum discrete signals.
Fig. 11 shows the result of performing polynomial (twenty-order) fitting on the spectral signal of the deuterium lamp, and it can be known from the result that the polynomial fitting is simple to implement, but has limited accuracy, and is not suitable for nonlinear approximation and disordered data containing singular values, i.e. light intensity calibration of a broadband micro spectrometer. Therefore, the cubic B-spline curve is more suitable for being used as a light intensity calibration algorithm of the broadband micro spectrometer.
Through comparison experiments, the real-time calibration method for the spectrum signal of the broadband spectrometer is proved to be suitable for wavelength calibration and light intensity calibration in the calibration process of the broadband spectrometer, and has real-time performance, practicability and higher accuracy.
It should be understood that the above description of the preferred embodiments is given for clarity and not for any purpose of limitation, and that various changes, substitutions and alterations can be made herein without departing from the spirit and scope of the invention as defined by the appended claims.
Claims (4)
1. A real-time calibration method for a spectrum signal of a broadband spectrometer is characterized by comprising the following steps:
step 1: constructing a measurement data point set of the spectral signal, and obtaining a maximum value point set of the spectral signal through a peak searching algorithm;
step 2: carrying out wavelength calibration by adopting a method of third-order polynomial fitting based on least square;
and step 3: carrying out parameterization on the pixel serial number of the spectral measurement data point by adopting a chord length parameterization method, then carrying out cubic B-spline curve fitting on the parameterized spectral measurement data point, and further carrying out sampling interpolation to finish the work of light intensity calibration;
and 4, step 4: establishing a corresponding relation between the wavelength and the light intensity according to the wavelength calibration and the light intensity calibration to finish the real-time calibration of the spectrum signal;
in step 4, the corresponding relationship between the wavelength and the light intensity is established as follows:
obtaining the wavelength y corresponding to the serial number x of the continuous pixel according to the wavelength calibration in the step 2, obtaining the light intensity z corresponding to the serial number x of the continuous pixel according to the light intensity calibration in the step 3, and obtaining the light intensity z corresponding to the wavelength y, namely:
(y,z),y∈[y1,y2]
thereby completing the real-time calibration of the spectrum signal, and y belongs to [ y ∈ [1,y2]Denoted as the spectrometer measurement band.
2. The real-time calibration method for the spectrum signal of the broadband spectrometer according to claim 1, characterized in that: the measurement data point set of the constructed spectrum signal in the step 1 is as follows:
collecting the spectrum signal by a broadband spectrometer, and collecting by a CCD camera in the broadband spectrometer to construct a measurement data point set of the spectrum signal:
U＝{(x0,z0),(x1,z1),...,(xN,zN)}
wherein (x)i,zi) N is the measurement data point of the ith spectral signal, N is the measurement data number of the spectral signal in the measurement data point set of the spectral signal, xiNumber of pixels, z, representing the ith spectral measurement data pointiThe light intensity of the ith spectral measurement data point is represented;
in the step 1, the maximum point set of the spectrum signal obtained by the peak searching algorithm is as follows:
according to a peak finding algorithm, z is compared sequentially by traversing a measurement data point set U of the spectrum signali-1,zi,zi+1If z is satisfiedi-1＜ziAnd z isi＞zi+1Namely, the maximum point, the obtained spectrum signal maximum point set, namely the peak position of the spectral line is as follows:
wherein the content of the first and second substances,
is the K thjThe measurement data point of each spectral signal is the jth spectral signal maximum, M is the number of spectral signal maximum in the set of spectral signal maximum,
denotes the K thjThe pixel serial number of the spectral measurement data point is the pixel serial number of the jth spectral signal maximum value point,
denotes the K thjThe light intensity of the jth spectral signal maximum value point is the light intensity of the spectral measurement data point.
3. The real-time calibration method for the spectrum signal of the broadband spectrometer according to claim 1, characterized in that: and 2, performing wavelength calibration by adopting a least square-based third-order polynomial fitting method as follows:
the measurement wave band of the spectrometer is y ∈ [ y >1,y2]Calibrating M characteristic spectral lines of light source in same wave band
As a benchmark;
wherein M is the number of the maximum points of the spectrum signal in the maximum point set of the spectrum signal, a0Is the first coefficient of a third-order polynomial, a1A second coefficient of a third-order polynomial, a2A third coefficient of a third order polynomial, a3A fourth coefficient that is a third order polynomial;
processing using least squares, points
The deviation of (a) is:
the least squares rule being to minimize the sum of squares of deviations
Namely, it is
To make it possible to
At minimum, for the independent variable a0、a1、a2、a3Calculating a partial derivative to make the value of the partial derivative be 0;
the wavelengths of M characteristic spectral lines of a calibration light source
And the pixel serial number of the corresponding spectrum signal maximum value point
Substituting the above formula to solve the coefficient solution of least square equation
Finally, the fitting formula of the pixel serial number and the wavelength is obtained as follows:
the corresponding relation between the serial number of the continuous pixel and the wavelength is obtained as follows:
where x ∈ [ x ]0,xN]Is the serial number of the continuous pixel, y belongs to [ y ∈ [)1,y2]Measuring the waveband for a spectrometer;
and (3) according to the step (1) and the step (2), the corresponding relation between the pixel serial number and the wavelength can be obtained, and the wavelength calibration work is completed.
4. The real-time calibration method for the spectrum signal of the broadband spectrometer according to claim 1, characterized in that: and 3, carrying out parameterization treatment on the pixel sequence numbers of the spectral measurement data points by adopting a chord length parameterization method:
pixel serial number x for N +1 spectral measurement data pointsiN, chord length parameterization:
wherein x isi-xi-1Is a chord edge vector, tiIs xiParameterized corresponding values;
total chord length of
Performing cubic B-spline curve fitting on the parameterized spectral measurement data points in step 3:
the cubic B-spline curve model is established as follows:
wherein, q is 0,1*，M*N is less than or equal to the number of nodes, PqTo control the node, Nq,3(t) is a 3-order canonical B-spline basis function, derived according to the recursion formula:
control node Pq,q＝1,2,...,M*-1 forming a node Matrix _ P having the following inverse equation relationship:
(Matrix_NTMatrix_N)Matrix_P＝Matrix_R
where i is 1, 2., N-1, and the Matrix _ R is a control node PqVector data matrix of RvIs the light intensity zvThe vector data difference of (a);
computation control node Pq,q＝1,2,...,M*A value of-1, modeled by a cubic B-spline curve, i.e. z0＝B(0)，zNB (1), can give P0、PM*Thus, a specific functional expression of a cubic B-spline fitting the curve B (t) can be obtained;
and step 3, further performing sampling interpolation to finish the work of light intensity calibration:
the cubic B-spline curve is sampled by selecting a proper sampling number H (H □ N) according to the requirement, and a series of discrete data points can be obtained
Comprises the following steps:
wherein L1/H-1 is a sampling interval, and a series of discrete data points are selected to obtain continuous light intensity data
As the reference for the light intensity fitting, there are:
wherein, L' ═ xN-x0the/H-1 is a serial number x of a continuous pixel, and x belongs to (x)0,xN) Interval of values of (1), connecting discrete data points in sequence
Continuous intensity data z can be acquired as follows:
thereby completing the light intensity calibration work.
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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 |
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