Correction method of Hadamard transform spectrometer

Abstract

The invention discloses a correction method for a Hadamard transform spectrometer, and relates to the technical field of optical imaging, and the method comprises the steps: S1, determining a Hadamard matrix, and constructing an ideal coding matrix; s2, obtaining an actual coding matrix from the ideal coding matrix according to the crosstalk influence model, namely S21, dividing the ideal coding matrix into a left ideal coding matrix and a right ideal coding matrix, determining a left actual coding coefficient and a right actual coding coefficient, and obtaining the left actual coding matrix, the right actual coding matrix and the actual coding matrix containing the coefficients; s22, establishing association among the left and right actual coding coefficients, the abnormal peak intensity value and the input spectrum; s23, measuring a group of input spectrums to obtain a measured value and an abnormal peak intensity value, calculating a left actual coding coefficient and a right actual coding coefficient, and obtaining an actual coding matrix; s3, when any spectrum is subjected to Hadamard coding measurement, the actual coding matrix is used for recovery, and a corrected spectrum is obtained. According to the method, the actual coding matrix is constructed and used for correcting spectral measurement, and the problem of measurement deviation caused by interference between wavelengths is solved.

Description

Technical Field

[0001] The invention relates to the technical field of optical imaging, and in particular to a correction method for a Hadamard transform spectrometer. Background Art

[0002] With its advantages of non-destructive analysis and rapid detection, near-infrared spectroscopy has become the main analytical tool in various scientific and industrial fields, and is widely used in agricultural production, food analysis, pharmaceutical industry, clinical medicine, materials science and other fields. The near-infrared spectrum band usually refers to the wavelength range between 780 and 2500nm. This spectral range is the frequency doubling and combined spectrum absorption band of the molecular vibration of various H-containing groups such as CH, NH, OH, SH in organic matter, and carries valuable information about the chemical composition and molecular structure of the sample. Therefore, it is particularly suitable for the analysis and identification of organic compounds, including polymers, foods, drugs and biological tissue samples.

[0003] With the continuous development of microcomputer technology, the miniaturization of NIR spectrometers has gradually become a research hotspot. DMD (Digital Micromirror Device) is a spatial light modulation device composed of many orderly arranged reflective micromirrors. Each micromirror can be individually encoded to control the light irradiated on it. It was initially widely used in projection, imaging and other fields. Later, researchers combined it with the Hadamard transform method and introduced it into the field of spectral analysis to design a Hadamard transform spectrometer based on DMD. Hadamard transform is a discrete linear orthogonal transform. It transforms the input vector through the Hadamard matrix and converts the data from the time domain or space domain to the column rate domain. Similar to Fourier transform, Hadamard transform can also realize frequency domain analysis of signals. Unlike Fourier transform, which uses sine and cosine basis functions for transformation, Hadamard transform uses orthogonal square wave basis functions, which is more suitable for change and frequency domain analysis in the field of digital discrete signals than Fourier transform.

[0004] The Hadamard transform spectrometer based on DMD uses DMD to perform Hadamard coding modulation with light dispersed by grating as incident light, encodes incident light of different wavelengths in the time domain with different Hadamard orthogonal sequences, and then performs Hadamard inverse transform on the measured time domain signal to obtain the intensity information of the spectrum from the Hadamard spectrum. Because each time domain signal measured by the detector is the result of coding multiplexing of all wavelengths, the intensity level of the detection signal is significantly improved, thereby achieving the purpose of improving the signal-to-noise ratio of spectral measurement, and being able to reliably measure weak signals. In addition, using DMD to replace the traditional mechanically moved coding mask can not only reduce the measurement error introduced by mechanical vibration and reduce the size of the spectrometer, but also break through the limitation that the coding matrix can only be a cyclic left-shifted quadratic residue structure Hadamard matrix, and introduce other Hadamard matrices for transform coding, such as a sequential Hadamard matrix with energy compression characteristics, which can achieve the purpose of shortening the spectral measurement time by sacrificing a certain spectral resolution. Therefore, the Hadamard transform spectrometer based on DMD has been widely used.

[0005] The use of DMD for Hadamard coding to measure spectra often results in inaccurate spectral measurements due to various reasons. In their research, Quan et al. divided spectral noise into multiplicative noise and time-correlation noise, and proposed corresponding denoising equations for different noises to improve the accuracy of spectral measurement. However, the two sets of correction matrices required by this method are difficult to obtain, and the time-correlation noise needs to be recalibrated in each measurement. Lu et al. adopted a dual filter strategy to effectively suppress stray light noise in spectral measurement, but each spectrum needs to be measured twice and then spliced. Based on the one-dimensional Hadamard coding spectrometer, Zhang et al. proposed a spectrometer for secondary encoding of Hadamard coefficients, which fully utilized the two-dimensional coding characteristics of DMD and combined with the coding matrix of complementary symmetric structure to effectively improve the spectral measurement speed and signal-to-noise ratio, but the two-dimensional coding is relatively complex.

[0006] It is worth pointing out that no literature has been found to analyze the problem of the deviation of the results of Hadamard transform spectrometers based on DMD (multiple wavelengths are encoded at the same time for each measurement) caused by the mutual influence of adjacent wavelength encodings and traditional scanning measurements based on DMD (only one wavelength is encoded for each measurement). The relative root mean square error of these two types of results can be as high as 5% in experiments. If not corrected, such a large deviation may lead to erroneous results in the measurement of trace samples and the comparison of similar samples. Summary of the invention

[0007] In view of the above problems, the present invention proposes a correction method for a Hadamard transform spectrometer. The present invention establishes a mathematical model for the inter-wavelength crosstalk of the spectrometer that produces measurement deviation, obtains the actual coding matrix, and uses the actual coding matrix to correct the measurement data. The method has good universality and is easy to implement, and can effectively reduce the spectral deviation of the Hadamard transform.

[0008] The calibration method of the Hadamard transform spectrometer is as follows:

[0009] S1, determine the Hadamard matrix, and construct an ideal coding matrix based on any column or row of the Hadamard matrix;

[0010] S2, according to the crosstalk impact model, the actual coding matrix is ​​obtained from the ideal coding matrix;

[0011] S3, when performing Hadamard coding measurement on an arbitrary spectrum, the actual coding matrix is ​​used to obtain the corrected restored spectrum.

[0012] Preferably, S2 comprises the following steps:

[0013] S21, dividing the ideal coding matrix into a left ideal coding matrix and a right ideal matrix according to the spatial position, determining the left actual coding coefficient and the right actual coding coefficient according to the inter-wavelength crosstalk phenomenon, modifying the left ideal coding matrix based on the left actual coding coefficient to obtain the left actual coding matrix, and modifying the right ideal coding matrix based on the right actual coding coefficient to obtain the right actual coding matrix; forming an actual coding matrix with coefficients from the left actual coding matrix and the right actual coding matrix;

[0014] S22, representing the coding sequence of the actual coding matrix containing the coefficients by using the Hadamard sequence of the Hadamard matrix to establish a correlation between the left actual coding coefficients, the right actual coding coefficients, the abnormal peak intensity value, and the input spectrum;

[0015] S23, use a spectrometer to perform Hadamard coding measurement on any set of input spectra, calculate the left actual coding coefficient value and the right actual coding coefficient value based on the obtained measured values ​​and the abnormal peak intensity values, and substitute them into the actual coding matrix containing the coefficients to obtain the actual coding matrix.

[0016] Preferably, in S21, the ideal coding matrix is ​​divided into a left ideal coding matrix and a right ideal matrix according to the spatial position, which is specifically expressed as:

[0017]

[0018] Where S represents the ideal coding matrix; S L represents the left ideal coding matrix, corresponding to the left half of the wavelength micromirror column; S R represents the right ideal coding matrix, corresponding to the right half of the wavelength micromirror column;

[0019] The actual coding matrix containing parameters composed of the left actual coding matrix and the right actual coding matrix is ​​expressed as:

[0020]

[0021] Among them, S′ represents the actual coding matrix containing coefficients; S′ L represents the left actual coding matrix; S′ R represents the right actual encoding matrix.

[0022] Preferably, in S21, the process of obtaining the left actual coding matrix and the right actual coding matrix is ​​specifically as follows:

[0023] Determine the left actual coding coefficients and obtain the left actual coding matrix:

[0024] The left ideal coding matrix contains n columns, one column corresponds to one wavelength; let each coding state of all wavelengths be affected only by the state of the micromirror of the wavelength on its left; for the non-zero elements in the j+1th column, if the element in the jth column of the same row is 1, the element in the j+1th column is affected, and the left actual coding coefficient l is used j represents the affected value of the non-zero element in the affected j+1th column; replace all the affected elements of the left ideal coding matrix with the left actual coding coefficients to obtain the left actual coding matrix;

[0025] Determine the right actual coding coefficients and obtain the right actual coding matrix:

[0026] The right ideal coding matrix contains n columns, one column corresponds to one wavelength; let each coding state of all wavelengths be affected only by the state of the micromirror of the wavelength on the right; for the non-zero elements in the jth column, if the elements in the j+1th column of the same row are 1, the elements in the jth column are affected, and the right actual coding coefficient r is used i represents the affected value of the non-zero element of the j-th column; replace all the affected elements of the right ideal coding matrix with the right actual coding coefficients to obtain the right actual coding matrix;

[0027] Wherein, j=1, 2, ..., n-1, n represents the number of all wavelengths to be encoded; the rows and columns of the above matrix can be interchanged without affecting the effectiveness of the method.

[0028] Preferably, in S22, the selected coding sequence is modified by substituting the coefficients into the crosstalk impact model, and the coding sequence of the actual coding matrix containing the coefficients is represented by the Hadamard sequence of the Hadamard matrix, and the formula is expressed as follows:

[0029]

[0030] Among them, S′ L(:, j+1) represents the coding sequence of the j+1th column in the left actual coding matrix; S′ R (:, j) represents the coding sequence of the jth column of the right actual coding matrix; H(:, 1) represents the Hadamard sequence of the first column of the Hadamard matrix; H Coding H represents the corresponding sequence in the Hadamard matrix that has the same coding waveform as the coding sequence S(:, j); Left_side H represents the Hadamard sequence corresponding to the sequence on the left that has a crosstalk effect on the coding sequence; Right_side The Hadamard sequence corresponding to the sequence on the right side that has a crosstalk effect on the coding sequence; H Abnormal Represents the Hadamard sequence corresponding to the abnormal peak.

[0031] Preferably, in S22, if the selected coding sequence is the corresponding coding sequence of all even sequence items of the Hadamard matrix, the coding sequence of the actual coding matrix containing the coefficients is represented by the corresponding Hadamard sequence in the Hadamard matrix, and the formula is expressed as follows:

[0032]

[0033] Among them, H(:, 2(j+1)) represents the Hadamard sequence of the 2(j+1)th column of the Hadamard matrix; H(:, 2j) represents the Hadamard sequence of the 2jth column of the Hadamard matrix.

[0034] Preferably, in S22, the association between the left actual coding coefficient, the right actual coding coefficient, the abnormal peak intensity value and the input spectrum is established as follows:

[0035] When n Hadamard sequences are used to encode the continuous n wavelengths of the input spectrum on the DMD, there are n-1 regions in the entire micromirror encoding region where the encoding sequences are adjacent to each other and produce abnormal peaks; the intensity value of each abnormal peak is expressed as d j , for the jth abnormal peak intensity value d j , are all composed of S′ L (:, j+1) and S′ R (:, j) for the spectral input value X = [x 1 , x 2 ,......,x n ] T x in j+1 and x j The common contribution of the encoded abnormal peaks is expressed as:

[0036]

[0037] Since the coding coefficients in the left actual coding matrix and the right actual coding matrix are continuous in the values ​​of adjacent points, let the relationship between the left actual coding coefficient and the right actual coding coefficient be lj =r j =f j , then the actual coding coefficient f j The calculation formula is:

[0038]

[0039] Preferably, after S2, the step further includes: verifying the obtained actual coding matrix, as follows:

[0040] Using a scanning measurement method of a spectrometer to measure a group of input spectra to obtain a first measured value, using a Hadamard measurement method of the spectrometer to measure the same group of input spectra to obtain a second measured value, and decoding the second measured value to obtain a measured column rate spectrum;

[0041] Encode the first measured value using the obtained actual coding matrix to obtain a simulated measured value; perform an inverse transformation on the simulated measured value to obtain a simulated column rate spectrum;

[0042] The relative root mean square error value between the measured column rate spectrum and the simulated column rate spectrum is calculated. If the relative root mean square error value is less than a preset percentage threshold, the actual coding matrix obtained meets the requirements.

[0043] Preferably, when performing Hadamard coding measurement on an arbitrary spectrum, the actual coding matrix is ​​used to obtain a corrected restored spectrum, which is expressed as:

[0044]

[0045] Among them, Y Test represents the measured value obtained by measuring the spectrum using Hadamard coding; Represents the actual encoding matrix The inverse matrix of Corrested represents the corrected recovered spectrum.

[0046] Preferably, the mask required by the Hadamard transform spectrometer is realized by a digital micromirror device (DMD).

[0047] Another correction method for a Hadamard transform spectrometer uses a zero insertion method to reduce the influence between adjacent codes based on the crosstalk phenomenon between wavelengths. Specifically, when encoding the input spectrum, a zero code row is set between the codes of every two adjacent wavelengths, or a zero code column is set between the codes of every two adjacent wavelengths; the number of the rows or columns is greater than or equal to 1.

[0048] Compared with the prior art, the present invention has the following beneficial effects:

[0049] The present invention uses the corrected actual coding matrix to perform an inverse transformation on the measured values ​​of the Hadamard coding measurement to obtain a corrected column rate spectrum. This method does not need to change the coding method and can retain the original spectral information to the greatest extent. It can also obtain a spectrum with more accurate measurement results without basically affecting the original signal-to-noise ratio advantage. In addition, the actual coding coefficient does not need to be repeatedly obtained, and the actual coding coefficient obtained by measuring a sample and the actual coding matrix can be directly used to restore the spectrum of other samples. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] The present invention is further described in detail below in conjunction with the accompanying drawings;

[0051] Figure 1 is a flow chart of a calibration method for a Hadamard transform spectrometer according to an embodiment of the present invention;

[0052] Figure 2 A structure diagram of a spectrometer of a calibration method for a Hadamard transform spectrometer according to an embodiment of the present invention;

[0053] Figure 3 The figure is a comparison diagram of the ideal Hadamard encoding result of the second measured value and the first measured value of the Hadamard encoding output domain spectrum of the Hadamard transform spectrometer of the embodiment of the present invention; wherein (a) represents the comparison between the measured data of the Hadamard encoding output result and its reference data; (b) represents the comparison between the column rate spectrum restored by the measured data and the reference spectrum;

[0054] Figure 4 A schematic diagram of abnormal peak intensities and coding coefficients at adjacent wavelengths of a calibration method for a Hadamard transform spectrometer according to an embodiment of the present invention;

[0055] Figure 5 The simulation of the Hadamard transform spectrum restored by the measured results of the calibration method of the Hadamard transform spectrometer of the embodiment of the present invention and the calibration spectrum obtained by using the correction matrix; wherein (a) represents the spectrum of the empty cuvette sample; (b) represents the spectrum of the water sample; (c) represents the spectrum of the alcohol sample; (d) represents the spectrum of the edible oil sample;

[0056] Figure 6 The calibrated column rate spectra obtained by the zero insertion method of the Hadamard transform spectrometer in the embodiment of the present invention are normalized to facilitate comparison of differences. Among them, (a) represents the spectrum of the empty cuvette sample; (b) represents the spectrum of the water sample; (c) represents the spectrum of the alcohol sample; and (d) represents the spectrum of the edible oil sample. DETAILED DESCRIPTION

[0057] The present invention is further described below through specific implementation modes.

[0058] See also Figure 1As shown in the figure, the calibration method of the Hadamard transform spectrometer is as follows:

[0059] This embodiment uses a NIR spectrometer (EVM, DLPNIRSCANEVM, TexasInstrument) from Texas Instruments for testing. The optical path is as follows: Figure 2 As shown. The light source of the spectrometer is a tungsten-halogen lamp (Tungsten-halogenlamp, L8008, INTERLIGHT). The broadband light it emits passes through the sample, then passes through a 25um*4.2mm slit, and then passes through a collimating lens and a bandpass filter with a passband of 1350-2450nm. It is then diffracted by a reflection grating and converged by a lens onto a digital micromirror device (DMD, DLP4500NIR, Texas Instrument). Each wavelength of light is irradiated onto the micromirrors in different column positions on the DMD, so the micromirrors are encoded in columns. When the encoding state of a column or several columns of micromirrors is "on", the light irradiated on these micromirrors is detected by a single-pixel InGaAs photodetector (InGaAs Photodetector, G12183-120K, Hamamatsu) through a collecting lens group.

[0060] S1, determine the Hadamard matrix, and construct an ideal coding matrix based on any column or row of the Hadamard matrix.

[0061] DMD scanning measurement mode and Hadamard coding measurement mode:

[0062] DMD is a spatial light modulation device that can control the collection of each tiny incident light beam that shines on the corresponding micromirror by individually encoding each micromirror. This is very consistent with the spectrum measurement method that uses Hadamard transform to multiplex and encode the spectrum. There are usually two measurement modes using DMD, one is scanning measurement and the other is Hadamard coding measurement.

[0063] Scanning measurement is to set the DMD micromirror to the "on" state in sequence along the wavelength expansion direction, and the detector records the intensity of each wavelength in sequence. The measurement results are as follows:

[0064]

[0065] Where X is the incident spectrum, E is the encoding matrix of the scanning measurement, and Y is the intensity value measured by the detector. In the scanning measurement mode, the value y received by the detector is i Equal to the intensity x of each wavelength iThe advantage of the scanning measurement method is that the measurement method is simple and the spectrum can be obtained without complex data processing. Therefore, the measured spectrum is used as a reference result in this study. Its disadvantages are low utilization of light sources, generally low detection signal intensity levels, greater noise influence, and poor signal-to-noise ratio.

[0066] Hadamard coding measurement uses the idea of ​​weighing design method. In order to accurately obtain the weight of multiple small objects, first measure the weight of the regular combination of multiple objects, because the accuracy of the instrument in measuring large physical quantities is much higher than that of measuring small physical quantities. Then, the weight of each small object is calculated and separated by mathematical methods. The combined measurement result is as follows:

[0067]

[0068] Among them, each row element of the S matrix (ideal coding matrix) represents the wavelength combination of a Hadamard coded data yi, and each column element of the matrix represents the coding sequence of each wavelength. S in Eq. (2) only selects the even-numbered columns in the 8th-order sequential Hadamard matrix (SOHM, Sequency-Ordered Hadamard Matrix), namely 2, 4, 6 and 8, as the coding sequences of the four wavelengths respectively. The reason why all sequence codes are not used in sequence is that selecting sequences with a certain carrier frequency interval like this can effectively reduce the mutual aliasing between coding sequences. Completing the other sequences of the S matrix and replacing the 0 values ​​in the matrix with -1 can obtain the corresponding 8th-order Hadamard matrix:

[0069]

[0070] Among them, from Eq. (2), it can be seen that the measurement data of basically each detector is They are all combinations of half the wavelength corresponding to the light intensity, so the Hadamard coding method has a high utilization rate of light intensity, thus having the advantages of high signal-to-noise ratio and anti-noise interference. Perform Hadamard inverse transform X′=H on the measured data Y -1 *Y, and the column rate spectrum X′ is obtained, where the value of the even column rate term is

[0071] Accuracy evaluation of spectral recovery using the Hadamard coding method:

[0072] In order to better evaluate the accuracy of spectral recovery, the spectrum measured by the scanning method is used as the reference spectrum of the sample, compared with the spectrum obtained by Hadamard encoding, and the relative root mean square error is calculated. The calculation formula of the relative root mean square error is as follows:

[0073]

[0074] Among them, xi is the reference value of the light intensity at the i-th wavelength measured using the scanning method, is the light intensity at the i-th wavelength measured using the Hadamard coding method. The smaller the relative RMS error, the more accurate the measured spectrum.

[0075] Comparison of the output results after Hadamard encoding using DMD and the corresponding spectrum recovery results with their respective reference values:

[0076] Figure 3 The output results of Hadamard encoding using DMD and the corresponding spectrum recovery results are compared with their respective reference values. Specifically, Figure 3 (a) is the comparison between the measured data of the Hadamard coding output and its reference data. The coding order refers to the sequence number of the Hadamard code on the DMD, that is, the sequence number of each row in the S matrix in Eq. (2), and the corresponding output is y in Eq. (2). i (y-axis is on the left). "Reference intensity" is the reference result of Hadamard transform directly on the spectrum obtained by scanning measurement method, and "measured intensity" is the actual measurement result after DMD encoding. "Deviation percentage" is the percentage deviation between the two. The corresponding y-axis is on the right.

[0077] Figure 3 (b) is the comparison between the column rate spectrum restored from the measured data and the reference spectrum. Each column rate corresponds to a column vector sequence of the Hadamard matrix. If the S matrix sequence of the Hadamard column vector corresponding to the column rate is used to encode a certain wavelength, its intensity will theoretically be equal to half of the intensity of the wavelength in the spectrum. The column rates with a large number of column rate values ​​close to zero in the "measured spectrum" data represent that this part of the sequence was not selected as the coding sequence, among which the marked prominent values ​​are non-coding sequences but their column rate intensity is not zero, that is, abnormal peaks.

[0078] For example, the sequence of all even-numbered columns of the 256-order S matrix (column rate is 2, 4, ..., 256) is used to encode the 128 wavelengths of light absorbed by the empty cuvette, and the exposure time for measuring each wavelength combination is 2000 μs. The actual measurement results of DMD encoding are as follows Figure 3 The reference value of the wavelength combination result is to substitute the spectrum X obtained by the scanning measurement method into Eq. (2) to obtain Y 理论参考 .Depend on Figure 3 (a) It can be seen that there is an obvious deviation between the actual coding results and their theoretical reference results. Figure 3The deviation percentage shown in (a) indicates that the deviation of the measured data at the beginning and end is the most obvious, and the measurement deviation in the middle is the smallest. Observing the DMD coding array corresponding to the data at these three locations (as shown in Eq. (2)), it is not difficult to find that the DMD coding at the beginning and end rows corresponds to the situation of measuring the combined intensity of consecutive adjacent wavelengths. At this time, when the coding appears multiple 1s continuously, as shown in The measurement deviation is quite obvious (>1%). The DMD code in the middle corresponds to the combined intensity of the measured interval wavelengths, and the codes 0 and 1 appear alternately, such as The measurement deviation is small (<1%).

[0079] Figure 3 The measured spectrum curve shown in (b) is the column rate spectrum obtained by Hadamard transforming the DMD measured data. After the Hadamard sequence is encoded, the wavelength intensity value of the spectrum will correspond to the column rate intensity of the encoded sequence in the column rate spectrum. Therefore, the reference spectrum can also be corresponded to the column rate and displayed in Figure 3 (b). The measured spectrum in the figure has obvious differences from the reference spectrum in the shape of the entire curve, and some of the column rate positions in the measured spectrum even have obvious abnormal peaks, such as Figure 3 The marked sequences in (b) belong to the Hadamard sequences that were not selected for wavelength encoding, indicating that sequence components that are not wavelength encoded and have obvious values ​​appear in the measured results of encoding.

[0080] S2, according to the crosstalk impact model, the actual coding matrix is ​​obtained from the ideal coding matrix.

[0081] S21, dividing the ideal coding matrix into a left ideal coding matrix and a right ideal matrix according to the spatial position, determining the left actual coding coefficients and the right actual coding coefficients according to the inter-wavelength crosstalk phenomenon, modifying the left ideal coding matrix based on the left actual coding coefficients to obtain the left actual coding matrix, and modifying the right ideal coding matrix based on the right actual coding coefficients to obtain the right actual coding matrix; forming an actual coding matrix with coefficients by the left actual coding matrix and the right actual coding matrix.

[0082] According to the distribution of the deviation percentage of the measured value, the following assumptions are made: when the wavelength is Hadamard-encoded on the DMD, for any coding combination displayed by the DMD, when the micromirror corresponding to a certain wavelength is set to the "on" state, it means that this wavelength needs to participate in the coding combination. The light intensity corresponding to this part of the micromirrors will be affected by the corresponding light intensity when the left and right micromirrors of the adjacent wavelengths are coded "on", causing a large degree of deviation in the measurement results after Hadamard coding, resulting in distortion of the spectrum recovery. When the wavelength coding combination appears as 0 and 1 intervals, that is, 0, 1, 0, 1, 0, 1, 0, 1, ..., the measurement deviation that occurs is basically negligible. Therefore, it is believed that when the wavelength code is 0, it has no effect on the output result of the code. Based on this phenomenon, a crosstalk influence model is established and an actual coding matrix is ​​proposed. The correctness of the assumption is verified by performing an inverse operation on it and observing whether the spectral accuracy can be improved.

[0083] First, because the actual coding coefficients of the micromirrors encoding each wavelength on the DMD will be affected by the coding of the two wavelengths on the left and right, the original ideal coding matrix is ​​modified:

[0084]

[0085] Among them, the left ideal coding matrix S L and the right ideal encoding matrix S R Each value in represents the ideal coding coefficient of the left and right half areas of the micromirror column of the corresponding wavelength; S is the ideal coding matrix, that is, the ideal coding coefficient is 1 or 0.

[0086] For example, taking the 8th-order S matrix used in Eq. (2) to encode 4 wavelengths using a sequential Hadamard matrix (SOHM),

[0087]

[0088] Each row corresponds to the DMD code at a different time, and each column corresponds to a different wavelength. The columns that are not used for coding in the traditional S matrix are not listed to avoid confusion. Although the DMD has two-dimensional pixels, considering that the grating in the spectrometer only splits light in one dimension, the DMD is encoded in one dimension here, and the code of each column of micromirrors is the same.

[0089] Since the actual coding matrix is ​​divided according to the spatial position, for S L For each element in the matrix, the encoding state of all wavelengths will only be affected by the state of the micromirror of the wavelength to its left. For example, if the element S(1,2) (row 1, column 2 of the S matrix) has an element S(1,1) to its left, then S L (1, 2) will be affected and become l 1, which means that its actual coding coefficient has changed due to the influence of the left micromirror state. Similarly, assuming that the actual coding coefficient of each column has changed in the same way when affected, the left ideal coding matrix S L Modified to the left actual coding matrix S′ L :

[0090]

[0091] Where L = [l 1 , l 2 , l 3 ] is the left actual coding coefficient matrix of the 2nd, 3rd and 4th columns after the change. Similarly, for S R The elements in the matrix, each encoding state of all wavelengths will only be affected by the state of the micromirror of the wavelength on the right, so the right ideal encoding matrix S R Modified to the right actual coding matrix S′ R :

[0092]

[0093] Where R = [r 1 , r 2 , r 3 ] is the right actual coding coefficient matrix of the 1st, 2nd and 3rd columns after the change. Assuming that the influence of the left and right adjacent wavelengths on the corresponding micromirrors is roughly the same, the final actual coding matrix containing coefficients can be obtained as follows:

[0094]

[0095] S22, representing the coding sequence of the actual coding matrix containing the coefficients by using the Hadamard sequence of the Hadamard matrix to establish a correlation between the left actual coding coefficients, the right actual coding coefficients, the abnormal peak intensity value, and the input spectrum;

[0096] In the ideal coding matrix S, each column element of the matrix represents the coding sequence for each wavelength. After the sequence is transformed by Hadamard, there will be two corresponding peaks in the Hadamard spectrum. Take the second column element of the S matrix, S(:, 2), as an example:

[0097]

[0098] Therefore, the coding sequence S(:, 2) will have values ​​at both the rate 1 and 4 positions in the rate spectrum. For any coding sequence S(:, j), we have:

[0099]

[0100] After each wavelength is encoded by a different coding sequence, the measured time domain results are subjected to an inverse Hadamard transform to obtain a Hadamard rate spectrum. The peak values ​​of different rate in the rate spectrum correspond to the intensities of each wavelength, and are therefore equivalent to a spectrum.

[0101] For S′ L and S′ R The peak positions of the coding sequences in the Hadamard spectrum will not be completely identical to those of S L and S R The corresponding coding sequence in Eq. (7) and Eq. (8) L (:,2) and S′ R (:, 2) as an example:

[0102]

[0103] S′ L (:,2) and S′ R There are 4 column rate values ​​in the column rate spectrum of (:, 2), of which the first two are S L (:,2) and S R (:, 2) inherent column rates 1 and 4, the third term is the column rates of the left and right coding sequences that affect the coding of this sequence, and the fourth term is Figure 3 The column rate positions corresponding to several abnormal peaks.

[0104] Extend this rule to S′ L , S′ R All even-numbered column encoding sequences in , then:

[0105]

[0106] Wherein, j=1, 2, ..., n-1, n is the number of all wavelengths to be encoded. L (:,1) and S′ R (:, n) is the sequence at the two ends and will not be affected by the adjacent coding sequence. Therefore, Eq. (14) and Eq. (15) do not contain these two items. The first two items in Eq. (14) and Eq. (15) are consistent with the two items in Eq. (11). The third item is the adjacent sequence that affects this sequence. The fourth item H Abnormal Represents the Hadamard sequence corresponding to the abnormal peak. Abnormal is a sequence of Hadamard matrices and cannot be further decomposed into a linear combination of multiple sequences, so each actual coding sequence only produces one abnormal peak in the column rate spectrum.

[0107] If the selected coding sequence is not limited to all even sequence items of the Hadamard matrix, the coding sequence of the actual coding matrix containing coefficients is represented by the Hadamard sequence of the Hadamard matrix, and the formula is expressed as follows:

[0108]

[0109] Among them, S′ L (:, j+1) represents the coding sequence of the j+1th column in the left actual coding matrix; S′ R (:, j) represents the coding sequence of the jth column of the right actual coding matrix; H(:, 1) represents the Hadamard sequence of the first column of the Hadamard matrix; H Coding H represents the corresponding sequence in the Hadamard matrix that has the same coding waveform as the coding sequence S(:, j); Left_side H represents the Hadamard sequence corresponding to the sequence on the left that has a crosstalk effect on the coding sequence; Right_side The Hadamard sequence corresponding to the sequence on the right side that has a crosstalk effect on the coding sequence; H Abnormal Represents the Hadamard sequence corresponding to the abnormal peak. The rows and columns of the above matrices can be interchanged without affecting the effectiveness of the method.

[0110] In addition, the abnormal peaks generated by different actual coding sequences are not exactly the same. When the sequence coding is determined, the column rate value of the abnormal peak in the column rate spectrum is also uniquely determined. In particular, when the coefficient interval between adjacent coding sequences is fixed to a specific value, the abnormal peaks generated will also repeat at several specific column rates in the column rate spectrum. If a sequence with a coefficient interval of 2 in a 256-order S matrix is ​​selected, that is, a sequence with a column rate of 2, 4, ..., 256, the wavelengths are encoded in turn. Calculated by Eq. (14) and Eq. (15), the abnormal peaks will repeat at column rates 3, 7, and 15, etc., which is consistent with Figure 3 (b) matches the column rate of the abnormal peak. Since the abnormal peaks appear repeatedly at certain column rates, they will accumulate into obvious values ​​in the column rate spectrum. When a sequence with a column rate of 2, 3, 4, ..., 129 in a 256-order S matrix is ​​selected to encode the same wavelength, it is calculated that the abnormal peaks appear repeatedly at column rates 2, 4, and 8. At this time, the column rate of the abnormal peak is the same as the column rate of some carrier frequency sequences, which will cause more serious crosstalk distortion in the restored spectrum.

[0111] When n Hadamard sequences are used to encode n consecutive wavelengths on the DMD, there are n-1 regions in the entire micromirror encoding region where the encoding sequences are adjacent to each other and produce abnormal peaks. Assume that the intensity of each abnormal peak (regardless of the abnormal peak position) is d j , then D=[d 1 , d 2 ,......,d n-1]. For any abnormal peak intensity value d i , are all composed of S′ L (:, j+1) and S′ R (:, j) for the spectrum X = [x 1 , x 2 ,......,x n ] j+1 、x j , the encoded abnormal peaks contribute together, and the corresponding correlation relationship is:

[0112]

[0113] Since S′ R and S′ L The continuity of the values ​​of adjacent points of the two sets of actual coding coefficients in , for the convenience of calculation, in Eq. (18) let:

[0114] l j =r j =f j

[0115] Therefore, Eq. (18) can be simplified as:

[0116]

[0117] Then the actual coding coefficient f j The calculation formula is:

[0118]

[0119] The calculation of the actual coding coefficient is extended to the entire spectrum measurement, and then:

[0120]

[0121] Where F = [f 1 , f 2 ,......,f n-1 ] represents the actual coding coefficient during actual coding, is the average intensity of adjacent points in the spectrum, D = [d 1 , d 2 ,......,d n-1 ] is the relative intensity of each abnormal peak at (n-1). The intensity of the abnormal peak generated by each pair of adjacent wavelength encoding is uniquely determined by the average intensity of the two pairs of adjacent wavelengths and the actual encoding coefficient after their mutual influence on the DMD.

[0122] S23, use a spectrometer to perform Hadamard coding measurement on any set of input spectra, calculate the left actual coding coefficient value and the right actual coding coefficient value based on the obtained measured values ​​and abnormal peak intensity values, and substitute them into the actual coding matrix containing the coefficients to obtain the actual coding matrix.

[0123] From Eq. (21), we can see that we only need to obtain a set of reference spectra X and the abnormal peak intensity D generated by adjacent wavelengths at each location to calculate the actual coding coefficient F during actual coding.

[0124] Since F reflects the actual coding coefficient change of the micromirrors at different positions on the DMD affected by the coding, the actual coding coefficient is determined when the position is determined. Therefore, although there are different abnormal peak intensities D for different reference spectra x, the coding coefficient F during actual coding should be the same. Substituting the coding coefficient F during actual coding into Eq. (9) yields the actual coding matrix (i.e. the numerical solution of S′).

[0125] The actual coding matrix obtained is verified and used to simulate the measured coding data, and then:

[0126]

[0127] Among them, X Reference is the reference spectrum measured using the scanning method, Y Simulated To simulate the measured data, Y Simulated Perform an inverse transformation to obtain the corresponding simulated column rate spectrum. Replace multiple different samples to obtain their reference spectra and measured spectra. If the measured column rate spectrum and the simulated column rate spectrum always match well (such as the relative root mean square error value is less than the preset percentage threshold), the correctness and universality of the model can be explained. The specific verification process can be seen in the experimental verification results of this embodiment.

[0128] S3, when performing Hadamard coding measurement on any spectrum, the actual coding matrix is ​​used to obtain the corrected restored spectrum.

[0129] If the actual encoding matrix If the measured data can be simulated well, it can be considered that:

[0130]

[0131] At this time, Y Test is the measured intensity value of the wavelength encoding by DMD. If the Hadamard inverse transform is performed directly, we get

[0132]

[0133] Among them, X′ TestThe even-numbered columns correspond to the intensity of each wavelength in the spectrum, that is, the recovered spectrum X Test .

[0134] Because Y Test The coding sequence It no longer corresponds to the Hadamard transform like the theoretical S matrix, X Test and the reference value X Reference There will also be deviations between Figure 3 observed in ).

[0135] At this time, the actual coding matrix can be used to decode the measured coded data, and then:

[0136]

[0137] Thus, the corrected recovery spectrum X is obtained Corrected .

[0138] The experimental verification results of this embodiment are as follows:

[0139] 1. Get the coding coefficient

[0140] Figure 4 The intensity statistics of abnormal peaks produced by actual coding measurement of each pair of adjacent wavelengths of the empty cuvette spectrum and the actual coding coefficient calculated by the intensity of the abnormal peak are shown. The sample used in the experiment is an empty cuvette. In the experiment, the absorption spectrum of 1350-2450nm is divided into 128 bands (λ 1 ,λ 2 , …, λ 128 ). Each measurement uses only the sequences with column rates of 2 and 4 in the 256-order S matrix to encode two adjacent wavelengths in sequence, i.e., λ 1 and λ 2 , 2 and λ 3 A total of 127 column rate spectra were measured and restored. A single measurement records the intensity values ​​of 256 coding combinations. The exposure time of a single coding combination is 2000μs, and the interval between two adjacent measurements is 30s. Since the coding sequence is determined, it can be seen from Eq. (14) and Eq. (15) that the column rate spectrum generated by encoding adjacent wavelengths with sequences of column rates 2 and 4 will have a unique abnormal peak at the column rate value of 3. The intensity values ​​of column rate 3 in the Hadamard column rate spectra of these 127 sets of measurement data are counted ( Figure 4 The solid line with a ball in the middle) is the abnormal peak intensity value D = [d 1 , d 2 ,......,d n-1Substituting the measured abnormal peak intensity into Eq. (21) we can obtain the actual coding coefficient F = [f 1 , f 2 ,......,f n-1 ]( Figure 4 dotted line).

[0141] 2. Coding coefficients simulation and recovery of actual measurements

[0142] Figure 5 The simulation of the measured recovery spectrum using the reference spectrum of the four samples and the correction recovery of the measured encoding results of the four samples are shown. Figure 4 Substitute the actual coding coefficient F obtained in S' L and S′ R Then we get the final actual coding matrix by As the coding matrix, the spectra of various samples obtained by the scanning measurement method are used as reference spectra and substituted into equation (22). Simulated Then perform the inverse Hadamard transform to obtain the simulated sequence rate spectrum, such as Figure 5 As shown in the “Simulated Spectrum” curve in . The “Simulated Spectrum” curve calculated by simulation and the “Measured Spectrum” curve of the column rate spectrum restored by the measured results not only have an excellent degree of agreement in the column rate of wavelength coding, but also can simulate the intensity value of the column rate corresponding to the abnormal peak very well. This phenomenon shows the correctness of the actual coding matrix model. And the coding coefficients obtained in a group of samples (empty cuvettes) can be used for the simulation of the measured restored column rate spectra of several other samples, which further verifies the correctness and universality of the coding coefficients. In addition, since the actual coding matrix for wavelength encoding on the DMD is obtained And verified the correctness of the model, so it can be The measured encoding results are corrected to obtain the corrected column rate spectrum.

[0143] Since the actual coding coefficient of the micromirror coding wavelength changes, the measured coding result Y Test The Hadamard frequency spectrum obtained by inverse transformation can no longer be directly restored using the ideal Hadamard transform method to obtain the frequency spectrum corresponding to the spectral intensity value. Instead, Y Test Substituting into the above Eq. (25), the calculated X Corrested like Figure 5 Compared with the "measured spectrum" curve of the column rate spectrum restored using the ideal Hadamard transform method, the "corrected spectrum" is obviously closer to the "reference spectrum".

[0144] Table 1 shows Figure 5 The relative root mean square error is compared between the ideal coding matrix recovery result (measured spectrum) and the actual coding matrix recovery result (corrected spectrum) and the reference spectrum. The smaller the relative root mean square error, the closer the recovered spectrum is to the reference spectrum. The error of the spectrum recovered using the correction matrix (i.e., the actual coding matrix) is significantly reduced, and the spectral accuracy is significantly improved.

[0145] Table 1: Comparison of spectral restoration results errors of different restoration methods.

[0146]

[0147] The corrected actual coding matrix is ​​used to inversely transform the measured data to obtain the corrected column rate spectrum. This method does not need to change the coding method and can retain the original spectral information to the greatest extent. It can also obtain a more accurate spectrum without basically affecting the original signal-to-noise ratio advantage. In addition, the coding coefficient does not need to be obtained repeatedly. The coding coefficient obtained by measuring a sample and the actual coding matrix can be directly used to restore the spectrum of other samples.

[0148] It is worth noting that the influence of interference between adjacent wavelengths can be reduced by increasing the distance between the micromirrors corresponding to the adjacent wavelength codes, that is, the zero insertion method, as follows:

[0149] The main reason for the deviation in spectral measurement is that the actual coding coefficient of the micromirror for light intensity changes due to the influence of the coding state of the adjacent micromirrors. Therefore, in addition to the aforementioned correction matrix method, the influence of this interference can also be reduced by increasing the distance between the micromirrors corresponding to the adjacent wavelength coding. The specific operation method is to set a column or row (or more columns / rows) of micromirrors that remain in the closed state during the entire measurement process between the micromirrors of different coding sequences. This part of the micromirrors will no longer participate in the Hadamard sequence encoding of the wavelength, which can effectively reduce the mutual influence of the coding coefficients between the coding sequences.

[0150] Figure 6 The spectrum measured by the zero insertion method is shown. The measured spectrum is close to the normalized reference spectrum after normalization, and the relative root mean square error is reduced to less than 1% compared with the uncorrected spectrum. The advantage of the zero insertion method is that it only needs to modify the state of some coded micromirrors, which is easy to implement, and the FWHT algorithm can still be used in subsequent data processing to achieve rapid processing of experimental data. The disadvantage is that the utilization rate of the micromirrors is reduced.

[0151] Table 2 shows the error comparison before and after correction of several other Hadamard coding methods using the correction matrix method and the zero insertion method. The Hadamard matrix used for encoding the spectrum on the DMD in this embodiment is the sequential Hadamard matrix (SOHM). In addition, the natural order Hadamard matrix (NOHM) and the quadratic residue structure Hadamard matrix (QRHM) are also widely used for spectral coding. Due to the similarity of the principles of several Hadamard coding methods, the actual coding coefficient of the micromirror on the wavelength intensity is affected by the adjacent coding sequence in these methods, which will also lead to serious measurement deviations. This deviation can also be corrected by the two methods proposed in this study. As shown in Table 2, the relative root mean square error of the spectrum obtained after correction by the correction matrix method and the zero insertion method is significantly improved compared with the uncorrected spectrum.

[0152] Table 2: Comparison of relative RMS errors of NOHM and QRHM matrix encoding before and after correction by the modified matrix method and zero insertion method.

[0153]

[0154] The data above are all intensity spectra. In practice, it is often necessary to obtain the absorption spectrum based on the spectrum of the empty cuvette and the intensity spectrum after adding the sample. From Eq. (24), we can see that X Test With X Reference (ieX in Eq.(2)) are related by a matrix. According to the Beer-Lambert Law, absorbance Among them, I Input is the incident light intensity, I Output is the intensity of the emitted light. Since it is impossible to measure I Input and I Output If you want to measure the absorption spectrum of a sample, you need to measure the transmission intensity spectrum X of the empty cuvette and the cuvette containing the sample. Empty and X Sample , and then substitute it into the absorption spectrum calculation formula to obtain the absorption spectrum of the sample. If the uncorrected measured intensity spectrum is used to calculate the absorption spectrum of the sample, then Therefore, if the uncorrected intensity spectrum is used to calculate the absorption spectrum, the influence of S′ in the absorption spectrum ratio obtained by matrix multiplication will not be offset, and there will be an obvious deviation from the reference spectrum ratio. However, using the corrected intensity spectrum for calculation can significantly reduce the deviation of the absorption spectrum.

[0155] In the process of studying the causes of abnormal peaks in the column rate spectrum, the wavelength carrier frequency sequence can be completely disrupted before encoding. At this time, the coefficient interval between the carrier frequency sequences encoding adjacent wavelengths will no longer be a fixed value. According to the model's definition of the abnormal peak column rate value, the abnormal peaks generated by each pair of adjacent coding sequences will no longer appear only at a few specific column rate values, so there will be no numerically obvious abnormal peaks in the column rate spectrum. However, the mutual influence between the coding sequences still exists, and there is still a large deviation between the restored spectrum and the reference spectrum. It's just that the abnormal peaks in the column rate spectrum are distributed in the full column rate spectrum in the form of many numerically smaller column rate components (the results are not shown due to space limitations).

[0156] It is worth noting that since the use of the correction matrix method and the zero insertion method can effectively eliminate abnormal peaks in the column rate spectrum, when selecting the carrier frequency sequence of the wavelength, a sequence of continuous column rate coefficients can be selected to increase the measurement speed. For example, when the sequence of the 2nd to 128th columns in the 128th order SOHM matrix is ​​used to encode 127 wavelengths, compared with the previous use of the sequence of the 2nd, 4th, 6th, ..., 256th columns in the 256th order SOHM matrix to encode 128 wavelengths, the sequence utilization rate of the column rate spectrum is increased from Promote to The new sequence selection method only needs to measure the coded combination data of 128 wavelengths, so the total measurement time will be reduced to half of the original time, while the spectral resolution remains basically unchanged.

[0157] The above is only a specific implementation of the present invention, but the design concept of the present invention is not limited thereto. Any non-substantial changes to the present invention using this concept shall be deemed as an infringement of the protection scope of the present invention.

Claims

1. A calibration method for a Hadamard transform spectrometer, characterized in that: The steps include: S1, determine the Hadamard matrix, and construct an ideal coding matrix based on any column or row of the Hadamard matrix; S2, according to the crosstalk impact model, the actual coding matrix is ​​obtained from the ideal coding matrix; S3, when performing Hadamard coding measurement on an arbitrary spectrum, the actual coding matrix is ​​used to obtain the corrected restored spectrum.

2. The calibration method of the Hadamard transform spectrometer according to claim 1, characterized in that: S2 includes the following steps: S21, dividing the ideal coding matrix into a left ideal coding matrix and a right ideal matrix according to the spatial position, determining the left actual coding coefficient and the right actual coding coefficient according to the inter-wavelength crosstalk phenomenon, modifying the left ideal coding matrix based on the left actual coding coefficient to obtain the left actual coding matrix, and modifying the right ideal coding matrix based on the right actual coding coefficient to obtain the right actual coding matrix; forming an actual coding matrix with coefficients from the left actual coding matrix and the right actual coding matrix; S22, representing the coding sequence of the actual coding matrix containing the coefficients by using the Hadamard sequence of the Hadamard matrix to establish a correlation between the left actual coding coefficients, the right actual coding coefficients, the abnormal peak intensity value, and the input spectrum; S23, use a spectrometer to perform Hadamard coding measurement on any set of input spectra, calculate the left actual coding coefficient value and the right actual coding coefficient value based on the obtained measured values ​​and the abnormal peak intensity values, and substitute them into the actual coding matrix containing the coefficients to obtain the actual coding matrix.

3. The calibration method of the Hadamard transform spectrometer according to claim 2, characterized in that: In S21, the ideal coding matrix is ​​divided into a left ideal coding matrix and a right ideal matrix according to the spatial position, which is specifically expressed as: Where S represents the ideal coding matrix; S L represents the left ideal coding matrix, corresponding to the left half of the wavelength micromirror column; S R represents the right ideal coding matrix, corresponding to the right half of the wavelength micromirror column; The actual coding matrix containing parameters composed of the left actual coding matrix and the right actual coding matrix is ​​expressed as: Among them, S ′ represents the actual coding matrix with coefficients; S L ′ represents the left actual coding matrix; S ′ R represents the right actual encoding matrix.

4. The calibration method of the Hadamard transform spectrometer according to claim 3, characterized in that: In S21, the process of obtaining the left actual coding matrix and the right actual coding matrix is ​​as follows: Determine the left actual coding coefficients and obtain the left actual coding matrix: The left ideal coding matrix contains n columns, one column corresponds to one wavelength; let each coding state of all wavelengths be affected only by the state of the micromirror of the wavelength on its left; for the non-zero elements in the j+1th column, if the element in the jth column of the same row is 1, the element in the j+1th column is affected, and the left actual coding coefficient l is used j represents the affected value of the non-zero element in the affected j+1th column; replace all the affected elements of the left ideal coding matrix with the left actual coding coefficients to obtain the left actual coding matrix; Determine the right actual coding coefficients and obtain the right actual coding matrix: The right ideal coding matrix contains n columns, one column corresponds to one wavelength; let each coding state of all wavelengths be affected only by the state of the micromirror of the wavelength on the right; for the non-zero elements in the jth column, if the elements in the j+1th column of the same row are 1, the elements in the jth column are affected, and the right actual coding coefficient r is used i represents the affected value of the non-zero element of the j-th column; replace all the affected elements of the right ideal coding matrix with the right actual coding coefficients to obtain the right actual coding matrix; Wherein, j=1, 2, ..., n-1, n represents the number of all wavelengths to be encoded; the rows and columns of the above matrix can be interchanged without affecting the effectiveness of the method.

5. The calibration method of the Hadamard transform spectrometer according to claim 4, characterized in that: In S22, the selected coding sequence is modified by substituting the coefficients into the crosstalk influence model, and the coding sequence of the actual coding matrix containing the coefficients is represented by the Hadamard sequence of the Hadamard matrix, and the formula is expressed as follows: Among them, S L ′ (:,j+1) represents the coding sequence of the j+1th column in the left actual coding matrix; S ′ R (:,j) represents the coding sequence of the jth column of the right actual coding matrix; H(:,1) represents the Hadamard sequence of the first column of the Hadamard matrix; H Coding represents the corresponding sequence in the Hadamard matrix that has the same coding waveform as the coding sequence S(:,j); H Left_side H represents the Hadamard sequence corresponding to the sequence on the left that has a crosstalk effect on the coding sequence; Right_side The Hadamard sequence corresponding to the sequence on the right side that has a crosstalk effect on the coding sequence; H Abnormal Represents the Hadamard sequence corresponding to the abnormal peak.

6. The calibration method of the Hadamard transform spectrometer according to claim 5, characterized in that: In S22, the association between the left actual coding coefficient, the right actual coding coefficient, the abnormal peak intensity value and the input spectrum is established as follows: When n Hadamard sequences are used to encode the continuous n wavelengths of the input spectrum on the DMD, there are n-1 regions in the entire micromirror encoding region where the encoding sequences are adjacent to each other and produce abnormal peaks; the intensity value of each abnormal peak is expressed as d j , for the jth abnormal peak intensity value d j , are all by S L ′ (:,j+1) and S ′ R (:,j) for the spectral input value X=[x1,x2,……,x n ] T x in j+1 and x j The common contribution of the encoded abnormal peaks is expressed as: Since the coding coefficients in the left actual coding matrix and the right actual coding matrix are continuous in the values ​​of adjacent points, let the relationship between the left actual coding coefficient and the right actual coding coefficient be l j =r j =f j , then the actual coding coefficient f j The calculation formula is:

7. The calibration method of the Hadamard transform spectrometer according to claim 1, characterized in that: After S2, the method further includes: verifying the actual encoding matrix obtained, as follows: Using a scanning measurement method of a spectrometer to measure a group of input spectra to obtain a first measured value, using a Hadamard measurement method of the spectrometer to measure the same group of input spectra to obtain a second measured value, and decoding the second measured value to obtain a measured column rate spectrum; Encode the first measured value using the obtained actual coding matrix to obtain a simulated measured value; perform an inverse transformation on the simulated measured value to obtain a simulated column rate spectrum; The relative root mean square error value between the measured column rate spectrum and the simulated column rate spectrum is calculated. If the relative root mean square error value is less than a preset percentage threshold, the actual coding matrix obtained meets the requirements.

8. The calibration method of the Hadamard transform spectrometer according to claim 1, characterized in that: When performing Hadamard coding measurement on an arbitrary spectrum, the actual coding matrix is ​​used to obtain the corrected restored spectrum, which is expressed as: Among them, Y Test represents the measured value obtained by measuring the spectrum using Hadamard coding; Represents the actual encoding matrix The inverse matrix of Corrected represents the corrected recovered spectrum.

9. The calibration method of the Hadamard transform spectrometer according to claim 1, characterized in that: The mask required for the Hadamard transform spectrometer is realized by a digital micromirror device (DMD).

10. A calibration method for a Hadamard transform spectrometer, characterized in that: According to the phenomenon of crosstalk between wavelengths, the zero insertion method is used to reduce the influence between adjacent codes; specifically: when encoding the input spectrum, a zero coding row is set between the codes of every two adjacent wavelengths, or a zero coding column is set between the codes of every two adjacent wavelengths; the number of the rows or columns is greater than or equal to 1.

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