CN110108694B - Method for improving wave number migration measurement precision of Raman spectrometer - Google Patents

Method for improving wave number migration measurement precision of Raman spectrometer Download PDF

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CN110108694B
CN110108694B CN201910414785.XA CN201910414785A CN110108694B CN 110108694 B CN110108694 B CN 110108694B CN 201910414785 A CN201910414785 A CN 201910414785A CN 110108694 B CN110108694 B CN 110108694B
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姚志湘
姚桔
粟晖
张景清
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Shanghai Ruhai Instrument Equipment Co ltd
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Guangxi University of Science and Technology
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Abstract

A method for improving the wave number migration measurement precision of a Raman spectrometer relates to a method for improving the spectral measurement precision, and comprises the following steps: 1) estimating wave number drift degree Rang of the spectrometer; 2) spectral measurement, interpolation and translation correction: decomposing a single measurement of long integration time into a plurality of small unit time measurements, selecting an initial unit as a reference, and performing uniform linear interpolation processing and translation correction on the reference and subsequent unit spectra; 3) spectrum merging, inverse difference value and calibrated wave number migration coordinate output: and (4) the series of unit spectra after the translation correction are accumulated into a single spectrum again, a plurality of single-row spectra are compared, the back difference value is adopted for trial calculation, the precision of an output instrument is redefined, the wave number migration coordinate is calibrated, and the measurement result is output. The invention can effectively improve the measurement precision of the Raman spectrum wave number, and the method is simple and convenient and is easy to popularize and apply.

Description

Method for improving wave number migration measurement precision of Raman spectrometer
Technical Field
The invention relates to a method for improving spectral measurement accuracy, in particular to a method for improving the wave number migration measurement accuracy of a Raman spectrometer.
Background
The accuracy of the measurement readings is an important indicator of the instrument. The reading precision of the migration wave number of a 2000-pixel instrument is about +/-0.5 wave number because a common array detector of the microminiature laser Raman spectrometer is limited by the number of pixel arrays. However, for some researches on the relationship between the Raman spectrum and temperature and pressure, more precise reading is needed, and a large Raman instrument with much higher price needs to be selected; or an interpolation method is adopted, but effective information is not added, so that the estimation accuracy is only improved by the direct interpolation effect, and the accuracy is not actually improved.
Measurement fluctuations caused by laser accuracy limitations are an important cause of the decrease in measurement accuracy. At present, the general index of Raman spectrum of the laser with acceptable cost is generally larger than +/-0.5 wave number, and is equivalent to the reading value of a pixel array, so that the driving force for selecting a higher pixel imaging element is also lacked when the instrument is designed and manufactured.
With the development of photosensitive devices, array detectors with higher pixels have become popular, such as CMOS arrays with more than 4000 pixels. There is a need for a method that can effectively improve the measurement accuracy and match it to perform its function.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: aiming at the requirement of exerting the performance of a high-pixel detector, a method for improving the wave number migration measurement precision of a Raman spectrometer is provided, and the aim of effectively improving the wave number measurement precision of the Raman spectrum is fulfilled.
Principle analysis:
the reading precision is influenced by a plurality of factors, and the laser Raman spectrometer can analyze from two aspects of the spectrometer and the laser light source. The array photosensitive spectrometer has no mechanical moving part, the optical path is fixed, so that the optical resolution is fixed, and after the spectrometer is thermally stable, the precision is mainly limited by noise influence and the number of pixel points. In the laser aspect, slight drift of the central wavelength and jitter of the peak width cause fluctuation of the excitation spectrum in a certain range, and the overall accuracy of the instrument is affected. Therefore, generally, the means for improving the precision is to try to improve pixel points, suppress noise and select a laser with better performance on hardware, which of course means cost improvement.
In principle, the shorter the duration of the same system, the smaller the fluctuations that occur, but on the other hand the poorer the signal-to-noise ratio of the signal, the more the system is affected by noise. For current raman measurements, signal to noise ratio tends to be of more concern. It is common practice to choose longer continuous measurement times to ensure signal-to-noise ratio without much concern for accuracy improvement. Long time measurements are advantageous for signal to noise ratio but do not improve the accuracy of the readings, even resulting in reduced accuracy.
The technical scheme of the invention is as follows: a method for improving the measurement precision of wave number migration of a Raman spectrometer comprises the following steps: 1) estimating wave number drift degree Rang of the spectrometer;
2) spectral measurement, interpolation and translation correction:
decomposing a single measurement of long integration time into a plurality of small unit time measurements, selecting an initial unit as a reference, and performing uniform linear interpolation processing and translation correction on the reference and subsequent unit spectra;
3) spectrum merging, inverse difference value and calibrated wave number migration coordinate output:
and (4) the series of unit spectra after the translation correction are accumulated into a single spectrum again, a plurality of single-row spectra are compared, the back difference value is adopted for trial calculation, the precision of an output instrument is redefined, the wave number migration coordinate is calibrated, and the measurement result is output.
The further technical scheme of the invention is as follows: the step 1) comprises the following specific methods:
1-1) for a set of selected Raman spectrometers, multiple measurements are made with a long integration time in a certain time period using a substance with a simple peak position, and the spectrum S of each measurement is recordedi
1-2) reading the pixel sequence number NP of the same peak position under each measurementiForm a sequenceNP=[NPi];
1-3) sequenceNPThe range of (d) is the abscissa drift degree Rang of the spectrometer in pixels.
The further technical scheme of the invention is as follows: the step 2) comprises the following specific methods:
2-1) decomposing a single measurement of the long integration time tl into a plurality of small unit times ts, and carrying out continuous unit time spectrum acquisition;
2-2) selecting the 1 St frame spectrum as a translation correction reference St; storing the subsequent acquisition unit spectrum S (i);
2-3) selecting ts/tl as a step length It value, centrally reading a unit spectrum S (i) from a stored subsequent unit spectrum, and performing linear interpolation with the same step length It interval as St to obtain a reference SIt after interpolation and a spectrum SI (i) to be corrected after interpolation;
2-4) SI (i) translation correction;
2-5) repeating the above steps 3) and 4) until all the unit spectra are corrected.
The further technical scheme of the invention is as follows: the step 2) comprises the following specific methods:
2-1) decomposing a single measurement of the long integration time tl into a plurality of small unit times ts, and carrying out continuous unit time spectrum acquisition;
2-2) selecting the spectrum of the 1 St frame as a translation correction reference St, and using the rest frames as unit spectra S (i) to carry out calibration by taking St as a reference;
2-3) selecting ts/tl as a step length It value, and performing linear interpolation on the unit spectra S (i) and S (t) by adopting the same step length It interval to obtain a reference SIt0 after interpolation and a spectrum SI (i) to be corrected after interpolation;
2-4) SI (i) translation correction;
2-5) repeating the above steps 3) and 4) until all the unit spectra are corrected.
The invention has the further technical scheme that: in the step 2-1), the small unit time ts is selected between 10 ms and 100ms by comprehensively considering the occurrence probability of instrument hot spots and the signal-to-noise ratio.
The invention has the further technical scheme that: the steps 2-4) comprise the following specific processes:
2-41) removing Nc values at the head and the tail of the sequence value of the reference SIt0 after interpolation to serve as a new reference SIt; where Nc is the value of M by Rang/It, i.e., the possible M-fold drift range of the spectrum, 1 < M < 10;
2-42) starting from the first value of SI (i), selecting a temporary sequence TS (1) according to the size of the reference SIt;
2-43) calculating the dot product of SIt and TS, if SIt and TS are both arranged in columns, DT (1) = SIt'. TS (1);
2-44, sequentially translating from SI (i) to TS (i) backwards to calculate DT (i) until the nth time, DT (n) reaches the maximum value, and TS (n) at the moment deviates the minimum from SIt;
2-45) storing TS (n) as new SI (i).
The invention has the further technical scheme that: the step 3) comprises the following specific steps:
3-1) will be corrected by translationThe latter multiple unit spectraSIRe-integration into a single spectrum according to integration time requirementsSOutputting;
3-2) for a plurality of single spectra over a period of timeSComparing, reducing interpolation interval trial calculation by adopting a spline interpolation contrast value, and redefining the precision of an output instrument according to the standard of plus and minus 1 reading interval;
3-3) in St or in a single spectrumSThe position of the Rayleigh center line contained in the spectrum, recalibrating the single spectrumSAnd outputting the measurement result according to the Raman migration wave number coordinate corresponding to each sequence value.
Due to the adoption of the technical scheme, compared with the prior art, the method for improving the wave number migration measurement precision of the Raman spectrometer has the following beneficial effects:
1. can effectively improve the measurement precision of Raman spectrum wave number
The invention comprises the following steps: 1) estimating wave number drift degree Rang of the spectrometer; 2) spectral measurement, interpolation and translation correction: decomposing a single measurement of long integration time into a plurality of small unit time measurements, selecting an initial unit as a reference, and performing uniform linear interpolation processing and translation correction on the reference and subsequent unit spectra; 3) spectrum merging, inverse difference value and calibrated wave number migration coordinate output: and (4) the series of unit spectra after the translation correction are accumulated into a single spectrum again, a plurality of single-row spectra are compared, the back difference value is adopted for trial calculation, the precision of an output instrument is redefined, the wave number migration coordinate is calibrated, and the measurement result is output. Wherein:
the invention decomposes the single measurement of long integration time into a plurality of small unit time measurements, so that the fluctuation of factors such as light sources and the like in each small unit is reduced; by selecting the starting unit as a reference, the subsequent units are subjected to translation correction and are unified to the reference, so that the fluctuation in the whole measurement period is also restrained; the invention also carries out uniform linear interpolation processing on the reference and the subsequent unit spectra, increases the number of steps of translational adjustment and can capture the tiny deviation of the spectra; and accumulating the series of units after the translation alignment to obtain a spectrogram with improved reading precision after interpolation for direct output. Therefore, the invention can effectively improve the measurement precision of the Raman spectrum wave number.
2. More sufficient information can be obtained
The invention obtains more sufficient information due to the expansion of the spectrum sampling frequency; and linear interpolation is introduced, and translation correction is combined, so that the acquired information can be retained at higher precision.
3. The method is simple and convenient, and is easy to popularize and apply.
The technical features of the method for improving the measurement accuracy of the wave number shift of the raman spectrometer according to the present invention will be further described with reference to the accompanying drawings and examples.
Drawings
FIG. 1: example one full-range spectrum measured multiple times over 10 minutes with a 1000ms integration time,
FIG. 2: FIG. 1 is a partially enlarged view;
FIG. 3: example one said carbon tetrachloride spectrum using 20 frames of 50ms spectral measurements,
FIG. 4: FIG. 3 is a partial enlarged view;
FIG. 5: example one 50 sets S of results corrected output over 10 minutes at 315cm-1An enlarged view of the peak of the wave,
FIG. 6: fig. 5 is a partially enlarged view.
Detailed Description
The first embodiment is as follows:
a method for improving the measurement precision of wave number migration of a Raman spectrometer comprises the following steps:
1) estimating the wave number drift degree Rang of the spectrometer:
1-1) for a selected set of Raman spectrometers, a simple peak position material such as carbon tetrachloride is used to perform multiple measurements over a period of time with a long integration time, and the spectrum S of each measurement is recordedi
1-2) reading the pixel sequence number NP of the same peak position under each measurementiForm a sequenceNP=[NPi];
1-3) sequenceNPIs the horizontal deviation of the spectrometer in pixelsThe degree of coordinate drift Rang;
2) spectral measurement, interpolation and translation correction:
2-1) decomposing a single measurement of the long integration time tl into a plurality of small unit times ts, and carrying out continuous unit time spectrum acquisition; comprehensively considering the occurrence probability of instrument hot spots and the signal-to-noise ratio, and selecting the small unit time ts between 10 and 100 ms;
2-2) selecting the 1 St frame spectrum as a translation correction reference St; storing the subsequent acquisition unit spectrum S (i);
2-3) selecting ts/tl as a step length It value, centrally reading a unit spectrum S (i) from a stored subsequent unit spectrum, and performing linear interpolation with the same step length It interval as St to obtain a reference SIt after interpolation and a spectrum SI (i) to be corrected after interpolation;
2-4) SI (i) translational correction:
2-41) removing Nc values at the head and the tail of the sequence value of the reference SIt0 after interpolation to serve as a new reference SIt; where Nc is the rounded value of M × Rang/It, i.e. the possible M times the drift range of the spectrum, M = 4;
2-42) starting from the first value of SI (i), selecting a temporary sequence TS (1) according to the size of the reference SIt;
2-43) calculating the dot product of SIt and TS, if SIt and TS are both arranged in columns, DT (1) = SIt'. TS (1);
2-44, sequentially translating from SI (i) to TS (i) backwards to calculate DT (i) until the nth time, DT (n) reaches the maximum value, and TS (n) at the moment deviates the minimum from SIt;
2-45) storing TS (n) as new SI (i);
2-5) repeating the steps 3) and 4) until the spectrum correction of all units is completed;
3) spectrum merging, inverse difference value and calibrated wave number migration coordinate output:
3-1) shift correcting multiple unit spectraSIRe-integration into a single spectrum according to integration time requirementsSOutputting;
3-2) for a plurality of single spectra over a period of timeSComparing, reducing interpolation interval trial calculation by spline interpolation contrast value, and calculating with positive and negative1 reading interval standard, redefining the precision of an output instrument;
3-3) in St or in a single spectrumSThe position of the Rayleigh center line contained in the spectrum, recalibrating the single spectrumSAnd outputting the measurement result according to the Raman migration wave number coordinate corresponding to each sequence value.
Example two:
a method for improving the measurement accuracy of wave number migration of a raman spectrometer, which is substantially the same as the first embodiment except that: the steps 2-2) and 2-3) are different.
The invention comprises the following steps:
1) estimating the wave number drift degree Rang of the spectrometer:
1-1) for a selected set of Raman spectrometers, a simple peak position material such as carbon tetrachloride is used to perform multiple measurements over a period of time with a long integration time, and the spectrum S of each measurement is recordedi
1-2) reading the pixel sequence number NP of the same peak position under each measurementiForm a sequenceNP=[NPi];
1-3) sequenceNPThe range of (1) is the abscissa drift degree Rang of the spectrometer in terms of pixels;
2) spectral measurement, interpolation and translation correction:
2-1) decomposing a single measurement of the long integration time tl into a plurality of small unit times ts, and carrying out continuous unit time spectrum acquisition; comprehensively considering the occurrence probability of instrument hot spots and the signal-to-noise ratio, and selecting the small unit time ts between 10 and 100 ms;
2-2) selecting the spectrum of the 1 St frame as a translation correction reference St, and using the rest frames as unit spectra S (i) to carry out calibration by taking St as a reference;
2-3) selecting ts/tl as a step length It value, and performing linear interpolation on the unit spectra S (i) and St by adopting the same step length It interval to obtain a reference SIt0 after interpolation and a spectrum SI (i) to be corrected after interpolation;
2-4) SI (i) translational correction:
2-41) removing Nc values at the head and the tail of the sequence value of the reference SIt0 after interpolation to serve as a new reference SIt; where Nc is the rounded value of M × Rang/It, i.e. the possible M times the drift range of the spectrum, M = 4;
2-42) starting from the first value of SI (i), selecting a temporary sequence TS (1) according to the size of the reference SIt;
2-43) calculating the dot product of SIt and TS, if SIt and TS are both arranged in columns, DT (1) = SIt'. TS (1);
2-44, sequentially translating from SI (i) to TS (i) backwards to calculate DT (i) until the nth time, DT (n) reaches the maximum value, and TS (n) at the moment deviates the minimum from SIt;
2-45) storing TS (n) as new SI (i);
2-5) repeating the steps 3) and 4) until the spectrum correction of all units is completed;
3) spectrum merging, inverse difference value and calibrated wave number migration coordinate output:
3-1) shift correcting multiple unit spectraSIRe-integration into a single spectrum according to integration time requirementsSOutputting;
3-2) for a plurality of single spectra over a period of timeSComparing, reducing interpolation interval trial calculation by adopting a spline interpolation contrast value, and redefining the precision of an output instrument according to the standard of plus and minus 1 reading interval;
3-3) by S (t) or single spectrumSThe position of the Rayleigh center line contained in the spectrum, recalibrating the single spectrumSAnd outputting the measurement result according to the Raman migration wave number coordinate corresponding to each sequence value.
The specific implementation case of the invention is as follows:
take the raman spectrum measurement of carbon tetrachloride on a certain raman spectrometer composed of 532nm laser and 4096 pixel CMOS photosensitive array as an example.
A method for improving the measurement precision of wave number migration of a Raman spectrometer comprises the following steps:
1) estimating the wave number drift degree Rang of the spectrometer:
1-1) measuring the Raman spectrum of carbon tetrachloride on a Raman spectrometer composed of 532nm laser and 4096 pixel CMOS photosensitive array for multiple times within 10 minutes in 1000ms integration time, and recordingRecording the spectrum S of each measurementi(ii) a FIG. 1 is a full range spectrum of multiple measurements over 10 minutes with an integration time of 1000ms, and FIG. 2 is a partial enlargement of FIG. 1;
1-2) reading the pixel sequence number NP of the same peak position under each measurementiForm a sequenceNP=[NPi];
1-3) sequenceNPThe range of (1) is the abscissa drift degree Rang of the spectrometer in terms of pixels;
the reading precision of the instrument is +/-0.7X wave number, and the peak value falls to 314.5 cm due to the fluctuation of the spectrum-1Or 316 cm-1See fig. 2. Even reading out the next bit X of ± 0.7X using interpolation does not increase the data accuracy due to pixel and spectral fluctuations. From direct measurement results, the spectral peak fluctuation drift degree Rang of the Raman spectrum of the instrument is 1 in terms of pixel within 10-minute measurement period, and the accuracy is more than +/-0.7 cm in terms of wave number-1
2) Spectral measurement, interpolation and translation correction:
2-1) the 1000ms integration time tl is decomposed into 50ms units, ts =50, i.e. the spectrum of the 1000ms integration time is replaced by 20 frames of 50ms spectral measurements for continuous unit time spectral acquisition. FIG. 3 is a carbon tetrachloride spectrum measured using a 20 frame 50ms spectrum, and FIG. 4 is a partial enlarged view of FIG. 3, with a peak fluctuation range of 3 pixels due to a short unit integration time and a reduced signal-to-noise ratio;
2-2) selecting the 1 St frame as a translation correction reference St, and taking the rest frames as S (i), and calibrating the spectrum of 19 frames in total by taking St as a reference;
2-3) selecting ts/tl as the value of the step size It, namely the step size is 1/20; performing linear interpolation on all the spectra in 1/20 steps to obtain a reference SIt0 after interpolation and a spectrum SI (i) to be corrected after interpolation;
2-4) SI (i) translational correction:
2-41) removing Nc values at the head and the tail of the sequence value of the reference SIt0 after interpolation to serve as a new reference SIt; where Nc is 4 × Rang/It =80, i.e. starting from the 80 th sequence point of SIt, 40000 points after selection are redefined as SIt.
2-42) starting from the first sequence point SI (1) of the rest SI (i), selecting 40000 points behind the first sequence point SI (1) as a temporary sequence TS (1) according to the size of SIt, and comparing with the SIt;
2-43) calculating the dot product of SIt and TS, if SIt and TS are both arranged in columns, DT (1) = SIt'. TS (1);
2-44, sequentially translating from SI (i) to TS (i) backwards to calculate DT (i) until the nth time, DT (n) reaches the maximum value, and TS (n) at the moment deviates the minimum from SIt;
2-45) storing TS (n) as new SI (i);
2-5) repeating the steps 3) and 4) until the spectrum correction of all units is completed;
3) spectrum merging, inverse difference value and calibrated wave number migration coordinate output:
3-1) the plurality of unit spectra SI are accumulated again into a single spectrum S to be output according to the requirement of integration time;
FIG. 5 is a graph of the results corrected for output in 10 minutes for 50 sets S at 315cm-1The peak deviation of the amplified situation graph of the peak is within +/-2 interpolation points;
3-2) comparing a plurality of single spectra S at reading intervals of 2, reducing interpolation interval trial calculation by adopting spline interpolation contrast values, redefining the precision of an output instrument according to the standard of positive and negative 1 reading intervals, and enabling the deviation of the output S peak value to be +/-1 interpolation serial number;
and 3-3) re-calibrating the Raman migration wave number coordinates corresponding to each sequence value of the single spectrum S according to the position of the Rayleigh central line contained in the St or the single spectrum S, and outputting the measurement result.
The Rayleigh peak reading after interpolation is 532.068nm, and the Raman shift coordinate is recalculated to be 315cm-1The adjacent interval of the position is less than +/-0.13, namely the data re-output after calibration has the precision of +/-0.13 cm-1
FIG. 6 shows the output result of FIG. 5 at 315cm-1Close up view of the vicinity, it can be seen that the spectral measurement accuracy within 10 minutes is from more than. + -. 0.7cm by the processing steps proposed by the present invention-1Lifting to less than +/-0.13 cm-1

Claims (4)

1. A method for improving the wave number migration measurement precision of a Raman spectrometer is characterized by comprising the following steps: the method comprises the following steps: 1) estimating wave number drift degree Rang of the spectrometer;
2) spectral measurement, interpolation and translation correction:
decomposing a single measurement of long integration time into a plurality of small unit time measurements, selecting an initial unit as a reference, and performing uniform linear interpolation processing and translation correction on the reference and subsequent unit spectra;
3) spectrum merging, inverse difference value and calibrated wave number migration coordinate output:
the series of unit spectra after the translation correction are accumulated into a single spectrum again, a plurality of single-row spectra are compared, trial calculation is carried out by adopting an inverse difference value, the precision of an output instrument is redefined, a wave number migration coordinate is calibrated, and a measurement result is output;
step 2) or the following specific method is included:
2-1) decomposing a single measurement of the long integration time tl into a plurality of small unit times ts, and carrying out continuous unit time spectrum acquisition;
2-2) selecting the 1 St frame spectrum as a translation correction reference St; storing the subsequent acquisition unit spectrum S (i);
2-3) selecting ts/tl as a step length It value, centrally reading a unit spectrum S (i) from a stored subsequent unit spectrum, and performing linear interpolation with the same step length It interval as St to obtain a reference Sit0 after interpolation and a spectrum SI (i) to be corrected after interpolation;
2-4) SI (i) translation correction;
2-5) repeating the steps 2-3) and 2-4) until all unit spectra are corrected;
step 2) or the following specific method is included:
2-1) decomposing a single measurement of the long integration time tl into a plurality of small unit times ts, and carrying out continuous unit time spectrum acquisition;
2-2) selecting the spectrum of the 1 St frame as a translation correction reference St, and using the rest frames as unit spectra S (i) to carry out calibration by taking St as a reference;
2-3) selecting ts/tl as a step length It value, and performing linear interpolation on the unit spectra S (i) and St by adopting the same step length It interval to obtain a reference SIt0 after interpolation and a spectrum SI (i) to be corrected after interpolation;
2-4) SI (i) translation correction;
2-5) repeating the steps 2-3) and 2-4) until all unit spectra are corrected;
the step 3) comprises the following specific steps:
3-1) shift correcting multiple unit spectraSIRe-integration into a single spectrum according to integration time requirementsSOutputting;
3-2) for a plurality of single spectra over a period of timeSComparing, reducing interpolation interval trial calculation by adopting a spline interpolation contrast value, and redefining the precision of an output instrument according to the standard of plus and minus 1 reading interval;
3-3) in St or in a single spectrumSThe position of the Rayleigh center line contained in the spectrum, recalibrating the single spectrumSAnd outputting the measurement result according to the Raman migration wave number coordinate corresponding to each sequence value.
2. The method for improving the measurement accuracy of the wave number migration of the Raman spectrometer according to claim 1, wherein the method comprises the following steps:
the step 1) comprises the following specific methods:
1-1) for a set of selected Raman spectrometers, multiple measurements are made with a long integration time in a certain time period using a substance with a simple peak position, and the spectrum S of each measurement is recordedi
1-2) reading the pixel sequence number NP of the same peak position under each measurementiForm a sequenceNP=[NPi];
1-3) sequenceNPThe range of (d) is the abscissa drift degree Rang of the spectrometer in pixels.
3. The method for improving the measurement precision of the wave number migration of the Raman spectrometer according to claim 2, wherein the method comprises the following steps: in the step 2-1), the small unit time ts is selected between 10 ms and 100ms by comprehensively considering the occurrence probability of instrument hot spots and the signal-to-noise ratio.
4. The method for improving the measurement precision of the wave number migration of the Raman spectrometer according to claim 2, wherein the method comprises the following steps: the steps 2-4) comprise the following specific processes:
2-41) removing Nc values at the head and the tail of the sequence value of the reference SIt0 after interpolation to serve as a new reference SIt; where Nc is the value of M by Rang/It, i.e., the possible M-fold drift range of the spectrum, 1 < M < 10;
2-42) starting from the first value of SI (i), selecting a temporary sequence TS (1) according to the size of the reference SIt;
2-43) calculating the dot product of SIt and TS, if SIt and TS are both arranged in columns, DT (1) = SIt'. TS (1);
2-44, sequentially translating from SI (i) to TS (i) backwards to calculate DT (i) until the nth time, DT (n) reaches the maximum value, and TS (n) at the moment deviates the minimum from SIt;
2-45) storing TS (n) as new SI (i).
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