A method and device for denoising Raman spectroscopy signals and a Raman spectrometer
By acquiring and processing Raman spectral signals, using a combination of addition and subtraction operations, the problem of random noise interference in Raman spectral signals is solved, and the signal-to-noise ratio and analysis accuracy are improved.
Patent Information
- Application Number
- CN202211338478.6
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2022-10-28
- Publication Date
- 2025-03-04
- Estimated Expiration
- 2042-10-28
AI Technical Summary
The prior art is difficult to effectively reduce the random noise interference in Raman spectral signals, especially under low light conditions, where the noise amplitude is large, resulting in a decrease in signal-to-noise ratio and affecting the accuracy of substance analysis.
By collecting reset signals and valid signals multiple times, performing addition operations separately, performing subtraction operations, and finally dividing by the number of samples N to obtain the actual pixel signal, thereby reducing the noise to process the Raman spectral signal.
Effectively eliminate reset noise and random noise, reduce noise interference to spectral signals, improve signal-to-noise ratio, and improve the accuracy of Raman spectral data for substance analysis.
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Figure CN115684129B_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the field of spectrum detection technology, and in particular to a Raman spectrum signal noise reduction processing method, device and Raman spectrometer. Background Art
[0002] Raman spectroscopy is a technique that detects the scattering spectrum of a substance when it is illuminated by monochromatic light. It can provide fast, simple, repeatable and non-destructive qualitative and quantitative analysis. In recent years, with the development of laser technology and CCD detection technology, Raman spectrometers have been widely used in structural detection and performance analysis of solid and liquid materials.
[0003] However, when Raman spectroscopy is used to detect substances, in addition to obtaining Raman signals containing the object to be detected, it will also be interfered by factors such as laser fluctuations, changes in the detection environment and the sample itself, generating noise to varying degrees. The noise signal of the Raman spectroscopy signal mainly comes from the CCD array detector, which mainly includes shot noise, dark current noise, reset noise, photon noise, etc. Dark current noise can be suppressed by cooling, and reset noise can be removed by double correlation sampling.
[0004] However, photon noise and shot noise are random, and the traditional double-correlation sampling method cannot reduce the interference of random noise on the spectral signal. Especially in low light conditions, the noise amplitude is large, which will cause the Raman spectrum to jitter and burr peaks to appear, and the signal-to-noise ratio of the spectrum will be reduced, thereby affecting the accuracy of Raman spectral data for material analysis. Therefore, how to improve the signal-to-noise ratio and avoid the interference of random noise on the spectral signal has become a major problem that needs to be solved urgently. Summary of the invention
[0005] In order to solve the problem that the random noise cannot be effectively filtered out in the above-mentioned prior art, the present invention provides a Raman spectroscopy signal noise reduction processing method, comprising the following steps:
[0006] Step S100, sampling the reset signal N times in sequence according to a preset interval time, where N ≥ 2, and performing an addition operation on the reset signals obtained by sampling to obtain a first signal; Step S200, sampling the valid signal N times in sequence according to the preset interval time, and performing an addition operation on the valid signals obtained by sampling to obtain a second signal; Step S300, subtracting the first signal from the second signal and dividing the result by N to obtain an actual pixel signal, which is the obtained noise-reduced signal.
[0007] In one embodiment, a CCD detector is used to collect Raman spectrum signals. The CCD detector is provided with a noise reduction circuit, and the steps S100, S200, and S300 are performed by the noise reduction circuit; the noise reduction circuit includes a first sampling circuit, a first adding circuit, a second sampling circuit, a second adding circuit, and a subtraction circuit; the first sampling circuit is connected in series with the first adding circuit to perform the step S100; the second sampling circuit is connected in series with the second adding circuit to perform the step S200; the first sampling circuit and the first adding circuit connected in series are connected in parallel with the second sampling circuit and the second adding circuit connected in series, and their parallel input ends are used to input sampling signals, and their parallel output ends are electrically connected to the subtraction circuit to perform the step S300.
[0008] In one embodiment, the first adding circuit includes a first operational amplifier and N first adding resistors, wherein the first ends of the N first adding resistors are connected in parallel and are electrically connected to the first sampling circuit, and the second ends are connected to the first input end of the first operational amplifier; the second input end of the first operational amplifier is grounded, and the output end of the first operational amplifier is connected to the subtraction circuit.
[0009] In one embodiment, the first sampling circuit includes N first switches and N first capacitors; each of the first switches is connected in series with a first adding resistor via a first capacitor to form N groups of sampling channels for collecting the reset signal.
[0010] In one embodiment, the second adding circuit includes a second operational amplifier and N second adding resistors; the first ends of the N second adding resistors are electrically connected to the second sampling circuit after being connected in parallel, and the second ends are connected to the first input end of the second operational amplifier; the second input end of the second operational amplifier is grounded, and the output end of the second operational amplifier is connected to the subtraction circuit.
[0011] In one embodiment, the second sampling circuit includes N second switches and N second capacitors; each of the second switches is connected in series with a second adding resistor via a second capacitor to form N groups of sampling channels for collecting the valid signal.
[0012] In one embodiment, the subtraction circuit includes a first subtraction capacitor, a second subtraction capacitor and a subtraction switch; the subtraction switch is connected in parallel between the first subtraction capacitor and the second subtraction capacitor, the first subtraction capacitor is electrically connected to the first addition circuit, and the second subtraction capacitor is electrically connected to the second addition circuit.
[0013] In one embodiment, the noise reduction circuit further includes a sampling capacitor, and the sampling capacitor is electrically connected to input ends of the first sampling circuit and the second sampling circuit connected in parallel.
[0014] The present invention also provides a Raman spectrum signal noise reduction processing device, comprising:
[0015] The first signal acquisition module is used to sample the reset signal N times through the CCD detector in sequence according to a preset interval time, where N≥2, and add the reset signals obtained by sampling to obtain a first signal; the second signal acquisition module is used to sample the effective signal N times through the CCD detector in sequence according to the preset interval time, and add the effective signals obtained by sampling to obtain a second signal; the actual pixel signal acquisition module is used to subtract the first signal from the second signal and divide the subtraction by N to obtain an actual pixel signal, and the actual pixel signal is the obtained noise-reduced signal.
[0016] The present invention further provides a Raman spectrometer, which adopts the Raman spectrum signal noise reduction processing method or the Raman spectrum signal noise reduction processing device as described in any of the above embodiments.
[0017] Based on the above, compared with the prior art, the Raman spectroscopy signal noise reduction processing method provided by the present invention can eliminate reset noise by collecting reset signals and valid signals multiple times and adding and then subtracting them, while also eliminating random noise, thereby reducing the interference of noise on spectral signals, improving the signal-to-noise ratio, and then effectively improving the accuracy of Raman spectroscopy data for material analysis.
[0018] Other features and beneficial effects of the present invention will be described in the following description, and partly become apparent from the description, or understood by practicing the present invention. The purpose and other beneficial effects of the present invention can be realized and obtained by the structures particularly pointed out in the description, claims and drawings. BRIEF DESCRIPTION OF THE DRAWINGS
[0019] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work. The positional relationships described in the drawings in the following description are based on the directions in which the components are drawn in the diagrams, unless otherwise specified.
[0020] Figure 1 A flowchart of the steps of the Raman spectroscopy signal noise reduction processing method provided by the present invention;
[0021] Figure 2 This is the circuit schematic diagram of the noise reduction circuit;
[0022] Figure 3 This is a schematic diagram of the structure of the Raman spectroscopy signal noise reduction processing device provided by the present invention.
[0023] Reference numerals:
[0024] 10 first sampling circuit 20 second sampling circuit 30 first adding circuit
[0025] 40 second adding circuit 50 subtracting circuit 31 first operational amplifier
[0026] 32 first summing resistor 11 first switch 12 first capacitor
[0027] 41 second operational amplifier 42 second summing resistor 21 second switch
[0028] 22 second capacitor 51 first subtraction capacitor 52 second subtraction capacitor
[0029] 53 subtraction switch 60 sampling capacitor DETAILED DESCRIPTION
[0030] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all the embodiments; the technical features designed in different implementation modes of the present invention described below can be combined with each other as long as they do not conflict with each other; based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.
[0031] In the description of the present invention, it should be noted that all terms used in the present invention (including technical terms and scientific terms) have the same meanings as those generally understood by ordinary technicians in the field to which the present invention belongs, and cannot be understood as limiting the present invention; it should be further understood that the terms used in the present invention should be understood to have the same meanings as these terms in the context of this specification and in the relevant fields, and should not be understood in an idealized or overly formal sense, unless explicitly defined in the present invention.
[0032] In the prior art, the double correlation sampling method is generally used to reduce the noise of Raman spectral signals. However, the traditional double correlation sampling method cannot effectively filter out the random noise, and under strong light, the signal amplitude of the Raman spectrum is large, and the traditional double correlation sampling method is not accurate in eliminating the reset noise. Under weak light, the effective signal amplitude of the Raman spectrum is small, and the random noise caused by it has a greater impact. The traditional double correlation sampling method has a worse noise reduction effect on random noise. Therefore, the present invention provides a Raman spectral signal noise reduction processing method, device and Raman spectrometer to effectively filter out random noise and reset noise, and reduce the interference of noise on the Raman spectral signal. The following is an explanation with a specific embodiment.
[0033] Embodiment 1
[0034] See also Figure 1 The present invention provides a method for denoising a Raman spectroscopy signal, comprising the following steps:
[0035] Step S100, sampling the reset signal N times in sequence according to a preset interval time, where N≥2, and performing an addition operation on the reset signals obtained by the sampling to obtain a first signal;
[0036] Step S200, sampling the valid signal N times in sequence according to a preset interval time, and performing an addition operation on the valid signals obtained by sampling to obtain a second signal;
[0037] Step S300, performing a subtraction operation on the first signal and the second signal and dividing the resultant signal by N to obtain an actual pixel signal, where the actual pixel signal is the obtained signal after noise reduction.
[0038] The above-mentioned method for denoising the Raman spectroscopy signal can eliminate reset noise and random noise at the same time, thereby reducing the interference of noise on the spectral signal, improving the signal-to-noise ratio, and then effectively improving the accuracy of Raman spectroscopy data for material analysis.
[0039] It should be noted that the preset interval time and the number of sampling times can be determined according to the actual duration of the reset signal generation, and are not limited here. Preferably, N is set to 3 or 4 or 5.
[0040] It should also be noted that the above-mentioned addition and subtraction operations on signals can be implemented not only by computer programs but also by hardware circuits. The hardware circuit is taken as an example below.
[0041] Preferably, a CCD detector is used to collect Raman spectrum signals, and a noise reduction circuit is provided in the CCD detector. Step S100, step S200, and step S300 are performed through the noise reduction circuit; the noise reduction circuit includes a first sampling circuit 10, a first adding circuit 30, a second sampling circuit 20, a second adding circuit 40, and a subtraction circuit 50; the first sampling circuit 10 is connected in series with the first adding circuit 30 to perform step S100; the second sampling circuit 20 is connected in series with the second adding circuit 40 to perform step S200; the first sampling circuit 10 and the first adding circuit 30 connected in series are connected in parallel with the second sampling circuit 20 and the second adding circuit 40 connected in series, and their parallel input ends are used to input sampling signals, and their parallel output ends are electrically connected to the subtraction circuit 50 to perform step S300.
[0042] Please refer to Figure 2 Specifically, the first adding circuit 30 includes a first operational amplifier 31 and N first adding resistors 32. After the N first adding resistors 32 are connected in parallel, the first ends are electrically connected to the first sampling circuit 10, and the second ends are connected to the first input end of the first operational amplifier 31; the second input end of the first operational amplifier 31 is grounded, and the output end of the first operational amplifier 31 is connected to the subtraction circuit 50. The first operational amplifier 31 is a voltage feedback operational amplifier or a current feedback operational amplifier.
[0043] The first sampling circuit 10 includes N first switches 11 and N first capacitors 12; each first switch 11 is connected in series with a first summing resistor 32 through a first capacitor 12 to form N groups of sampling channels for collecting reset signals. The specific sampling control method is to control the on and off of the N first switches 11 in sequence according to a preset interval time to store the reset signal in the N first capacitors 12.
[0044] The second adding circuit 40 includes a second operational amplifier 41 and N second adding resistors 42; the first ends of the N second adding resistors 42 are electrically connected to the second sampling circuit 20 after being connected in parallel, and the second ends are connected to the first input end of the second operational amplifier 41; the second input end of the second operational amplifier 41 is grounded, and the output end of the second operational amplifier 41 is connected to the subtraction circuit 50. The second operational amplifier 41 is a voltage feedback operational amplifier or a current feedback operational amplifier.
[0045] The second sampling circuit 20 includes N second switches 21 and N second capacitors 22; each second switch 21 is connected in series with a second adding resistor 42 through a second capacitor 22 to form N groups of sampling channels for collecting valid signals. The specific sampling control method is to control the on and off of the N second switches 21 in sequence according to the preset interval time to store the valid signal in the N second capacitors 22.
[0046] The subtraction circuit 50 includes a first subtraction capacitor 51, a second subtraction capacitor 52 and a subtraction switch 53; the subtraction switch 53 is connected in parallel between the first subtraction capacitor 51 and the second subtraction capacitor 52, the first subtraction capacitor 51 is electrically connected to the first addition circuit 30, and the second subtraction capacitor 52 is electrically connected to the second addition circuit 40. The first subtraction capacitor 51 is used to store the first signal obtained by the first addition circuit 30 in the first subtraction capacitor 51, the second subtraction capacitor 52 is used to store the second signal obtained by the second addition circuit 40 in the second subtraction capacitor 52, and the subtraction switch 53 is used to perform a subtraction operation between the first signal and the second signal in the first subtraction capacitor 51 and the second subtraction capacitor 52.
[0047] Preferably, the noise reduction circuit further includes a sampling capacitor 60 , and the sampling capacitor 60 is electrically connected to input ends of the first sampling circuit 10 and the second sampling circuit 20 connected in parallel.
[0048] It should be noted that the specific types of the first sampling circuit 10 and the second sampling circuit 20 are not unique. In one embodiment, they can be implemented by switches and capacitors. In other embodiments, they can also be implemented by resistor voltage divider sampling circuits or filter circuits. In addition to the above-mentioned circuits and their necessary components, those skilled in the art can also improve the sampling circuit, addition circuit, and subtraction circuit according to actual needs, and add other functional circuits or circuit elements such as filter circuits, all of which fall within the protection scope of the present invention.
[0049] In summary, the specific control method of the noise reduction circuit is as follows: (1) disconnecting the N second switches 21 and the subtraction switch 53, turning on the N first switches 11 in turn according to the preset interval time, and storing the reset signal in the N first capacitors 12, and the N first capacitors 12 input all the collected reset signals into the first operational amplifier 31 through the first summing resistor 32 for addition processing to obtain the first signal and store it in the first subtraction capacitor 51; (2) disconnecting the N first switches 11 and the subtraction switch 53, turning on the N second switches 21 in turn according to the preset interval time, and storing the valid signal in the N second capacitors 22, and the N second capacitors 22 input all the collected valid signals into the second operational amplifier 41 through the second summing resistor 42 for addition processing to obtain the second signal and store it in the second subtraction capacitor 52; (3) disconnecting the N first switches 11 and the N second switches 21, closing the subtraction switch 53, and realizing the subtraction processing of the first signal and the second signal.
[0050] Furthermore, the actual pixel signal can be obtained by dividing the result obtained by the subtraction process by N. The actual pixel signal can be obtained by transmitting the result to a microprocessor, which performs a division operation.
[0051] Embodiment 2
[0052] See also Figure 3 The present invention also provides a Raman spectrum signal noise reduction processing device, comprising:
[0053] The first signal acquisition module is used to sample the reset signal N times through the CCD detector in sequence according to a preset interval time, where N≥2, and add the reset signals obtained by the sampling to obtain a first signal; the second signal acquisition module is used to sample the effective signal N times through the CCD detector in sequence according to a preset interval time, and add the effective signals obtained by the sampling to obtain a second signal; the actual pixel signal acquisition module is used to subtract the first signal from the second signal and divide the subtraction by N to obtain an actual pixel signal, which is the obtained noise-reduced signal.
[0054] Specifically, each module can be implemented in whole or in part by computer program software or hardware circuits and their combination. For details, please refer to the hardware circuit design method of embodiment 1, which will not be repeated here. In addition, the above modules can be embedded in or independent of the processor of the computer device in the form of hardware, or can be stored in the memory of the computer device in the form of software, so that the processor can call and execute the operations corresponding to the above modules.
[0055] Embodiment 3
[0056] The present invention also provides a Raman spectrometer, which adopts the Raman spectrum signal noise reduction processing method or the Raman spectrum signal noise reduction processing device of any of the above embodiments. Preferably, the Raman spectrometer includes a CCD detector and a processing module, and the CCD detector is provided with a noise reduction circuit, and the noise reduction circuit is electrically connected to the processing module. The Raman spectrum signal noise reduction processing method of any of the above embodiments can be implemented by the cooperation of the noise reduction circuit and the processing module. For details, please refer to the first embodiment, which will not be described in detail here.
[0057] In summary, the Raman spectral signal noise reduction processing method, device and Raman spectrometer provided by the present invention can effectively and accurately filter out reset noise and random noise from the acquired Raman spectral signal, avoid noise interference on the spectral signal, improve the signal-to-noise ratio, and then effectively improve the accuracy of Raman spectral data for material analysis.
[0058] In addition, those skilled in the art should understand that, although there are many problems in the prior art, each embodiment or technical solution of the present invention can be improved in only one or several aspects, without having to solve all the technical problems listed in the prior art or background technology at the same time. Those skilled in the art should understand that the content not mentioned in a claim should not be used as a limitation on the claim.
[0059] Although the terms such as preset interval time, reset signal, valid signal, first signal, second signal, actual pixel signal, noise reduction circuit, first sampling circuit, second sampling circuit, first adding circuit, second adding circuit, subtracting circuit, first signal acquisition module, second signal acquisition module, actual pixel signal acquisition module, etc. are used more frequently in this article, the possibility of using other terms is not excluded. The use of these terms is only to more conveniently describe and explain the essence of the present invention; interpreting them as any additional restrictions is contrary to the spirit of the present invention; the terms "first", "second", etc. (if any) in the description and claims of the embodiments of the present invention and the above-mentioned drawings are used to distinguish similar objects, and are not necessarily used to describe a specific order or sequence.
[0060] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.
Claims
1. A method for denoising a Raman spectroscopy signal, characterized in that: The following steps are involved: Step S100, sampling the reset signal N times in sequence according to a preset interval time, where N≥2, and performing an addition operation on the reset signals obtained by sampling to obtain a first signal; Step S200, sampling the valid signal N times in sequence according to the preset interval time, and performing an addition operation on the valid signals obtained by sampling to obtain a second signal; Step S300, performing a subtraction operation on the first signal and the second signal and dividing the resultant signal by N to obtain an actual pixel signal, wherein the actual pixel signal is the obtained signal after noise reduction; A CCD detector is used to collect Raman spectrum signals, wherein a noise reduction circuit is provided in the CCD detector, and the step S100, the step S200, and the step S300 are performed by the noise reduction circuit; The noise reduction circuit includes a first sampling circuit, a first adding circuit, a second sampling circuit, a second adding circuit and a subtracting circuit; The first sampling circuit is connected in series with the first adding circuit to perform the step S100; the second sampling circuit is connected in series with the second adding circuit to perform the step S200; the first sampling circuit and the first adding circuit connected in series are connected in parallel with the second sampling circuit and the second adding circuit connected in series, and their parallel input ends are used to input sampling signals, and their parallel output ends are electrically connected to the subtraction circuit to perform the step S300; The first adding circuit includes a first operational amplifier and N first adding resistors. After the N first adding resistors are connected in parallel, the first ends are electrically connected to the first sampling circuit, and the second ends are connected to the first input end of the first operational amplifier; the second input end of the first operational amplifier is grounded, and the output end of the first operational amplifier is connected to the subtraction circuit; the second adding circuit includes a second operational amplifier and N second adding resistors; after the N second adding resistors are connected in parallel, the first ends are electrically connected to the second sampling circuit, and the second ends are connected to the first input end of the second operational amplifier; the second input end of the second operational amplifier is grounded, and the output end of the second operational amplifier is connected to the subtraction circuit; the subtraction circuit includes a first subtraction capacitor, a second subtraction capacitor and a subtraction switch; the subtraction switch is connected in parallel between the first subtraction capacitor and the second subtraction capacitor, the first subtraction capacitor is electrically connected to the first adding circuit, and the second subtraction capacitor is electrically connected to the second adding circuit.
2. The method for denoising a Raman spectroscopy signal according to claim 1, characterized in that: The first sampling circuit includes N first switches and N first capacitors; each of the first switches is connected in series with a first adding resistor via a first capacitor to form N groups of sampling channels for collecting the reset signal.
3. The method for denoising a Raman spectroscopy signal according to claim 1, wherein: The second sampling circuit includes N second switches and N second capacitors; each of the second switches is connected in series with a second adding resistor via a second capacitor to form N groups of sampling channels for collecting the effective signal.
4. The method for denoising a Raman spectroscopy signal according to any one of claims 1 to 3, characterized in that: The noise reduction circuit further includes a sampling capacitor, and the sampling capacitor is electrically connected to input ends of the first sampling circuit and the second sampling circuit connected in parallel.
5. A Raman spectroscopy signal noise reduction processing device, characterized in that: include: A first signal acquisition module, configured to sample the reset signal N times in sequence through a CCD detector according to a preset interval time, where N ≥ 2, and perform an addition operation on the reset signals obtained by sampling to obtain a first signal; A second signal acquisition module, configured to sample the effective signal N times in sequence through the CCD detector according to the preset interval time, and perform addition operation on the effective signals obtained by sampling to obtain a second signal; an actual pixel signal acquisition module, configured to perform a subtraction operation on the first signal and the second signal and then divide the resultant signal by N to obtain an actual pixel signal, wherein the actual pixel signal is the obtained signal after noise reduction; The CCD detector is provided with a noise reduction circuit, and the noise reduction circuit includes a first sampling circuit, a first adding circuit, a second sampling circuit, a second adding circuit and a subtracting circuit; The first sampling circuit is connected in series with the first adding circuit; the second sampling circuit is connected in series with the second adding circuit; the first sampling circuit and the first adding circuit connected in series are connected in parallel with the second sampling circuit and the second adding circuit connected in series, and their parallel input ends are used to input sampling signals, and their parallel output ends are electrically connected to the subtraction circuit; The first adding circuit includes a first operational amplifier and N first adding resistors. After the N first adding resistors are connected in parallel, the first ends are electrically connected to the first sampling circuit, and the second ends are connected to the first input end of the first operational amplifier; the second input end of the first operational amplifier is grounded, and the output end of the first operational amplifier is connected to the subtraction circuit; the second adding circuit includes a second operational amplifier and N second adding resistors; after the N second adding resistors are connected in parallel, the first ends are electrically connected to the second sampling circuit, and the second ends are connected to the first input end of the second operational amplifier; the second input end of the second operational amplifier is grounded, and the output end of the second operational amplifier is connected to the subtraction circuit; the subtraction circuit includes a first subtraction capacitor, a second subtraction capacitor and a subtraction switch; the subtraction switch is connected in parallel between the first subtraction capacitor and the second subtraction capacitor, the first subtraction capacitor is electrically connected to the first adding circuit, and the second subtraction capacitor is electrically connected to the second adding circuit.
6. A Raman spectrometer, characterized in that: The Raman spectroscopy signal denoising processing method according to any one of claims 1 to 4 or the Raman spectroscopy signal denoising processing device according to claim 5 is adopted.
Citation Information
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