CN113176249B - Quick Raman scanning imager - Google Patents

Quick Raman scanning imager Download PDF

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CN113176249B
CN113176249B CN202110552768.XA CN202110552768A CN113176249B CN 113176249 B CN113176249 B CN 113176249B CN 202110552768 A CN202110552768 A CN 202110552768A CN 113176249 B CN113176249 B CN 113176249B
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raman
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laser
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CN113176249A (en
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邢金玉
邵鹏飞
郑致远
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University of Science and Technology of China USTC
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    • G01MEASURING; TESTING
    • G01NINVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N21/00Investigating or analysing materials by the use of optical means, i.e. using sub-millimetre waves, infrared, visible or ultraviolet light
    • G01N21/62Systems in which the material investigated is excited whereby it emits light or causes a change in wavelength of the incident light
    • G01N21/63Systems in which the material investigated is excited whereby it emits light or causes a change in wavelength of the incident light optically excited
    • G01N21/65Raman scattering
    • G01N21/658Raman scattering enhancement Raman, e.g. surface plasmons

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Abstract

The invention discloses a rapid Raman scanning imager which comprises a spectrometer, a laser and a light excitation and acquisition module, wherein a Raman enhancement substrate is arranged on a focal plane of a scanning field lens in the light excitation and acquisition module, and an object to be measured is attached to the Raman enhancement substrate and is adsorbed by the Raman enhancement substrate. The invention realizes the scanning operation mode without focusing and reduces the scanning imaging time; the three-dimensional network structure of the Raman enhanced substrate is utilized to adsorb the fluid or micro-granular object to be measured on the substrate and fix the fluid or micro-granular object to be measured on the focal plane of the scanning field lens, so that the displacement of the object in each scanning point is limited, and the measurement precision is improved.

Description

Quick Raman scanning imager
Technical Field
The present invention relates to raman imagers, and more particularly to fast raman imagers particularly suited for use in the technical field of accurate material identification on material surfaces.
Background
Raman light is a scattering phenomenon. When the excitation light irradiates on the object to be measured, the spectrum of the generated Raman scattering signal is analyzed to obtain the molecular components forming the substance to be measured. Surface enhanced raman spectroscopy is a technique that enhances the raman scattering signal by coupling with the object under inspection at the surface of a roughened material with nanoscale structures. The enhancement effect of the method is generally up to multiple orders of magnitude, and the method has sensitivity close to single molecule, so that the method is widely applied to substance trace detection.
Common raman spectrometers have very high requirements on the diameter of the excitation light spot: the smaller the spot diameter is, the better, take the laser with the wavelength of 785nm as an example, under ideal conditions, when the spectral resolution reaches 0.6nm, the maximum diameter of the spot is only 150um, and the depth of the laser spot is also limited to about tens of microns to 100 microns along the laser irradiation direction near the laser focusing mirror focal plane of the raman probe. The Raman probe is mainly caused by the influence of the structures of the existing spectrometer and the Raman probe and the Raman light generated by objects near the point to be measured on the Raman light signal of the point to be measured.
In the field of point-scan raman detection, two key problems currently exist: firstly, the focusing process greatly prolongs the measurement time, and because the prior art limits the diameter of a light spot and the position variation of a point to be measured and the point to be measured cannot be generally distributed on a plane, almost every measurement point needs to be focused again to obtain the optimal Raman signal, and the scanning process is as follows: planning a measuring path, pre-focusing, directing a scanning galvanometer to a measuring point on the planned path, focusing, acquiring a signal, and then measuring a next measuring point …; in the process, a large amount of measurement time is wasted in a focusing link, and the measurement time is limited, so that the method is difficult to adapt to application scenes with high real-time requirements, such as real-time measurement of the content of microorganisms; secondly, because the displacement of the object to be measured generates a measurement error, for many measurement fields, such as biological tissue surface substance detection, fluid surface substance detection and the like, the object to be measured or an object attached to the object to be measured has certain mobility, after focusing is completed, the object to be measured in each scanning point still generates certain unpredictable displacement in the measurement process, and when the displacement exceeds dozens of micrometers, a measurement signal is rapidly reduced; due to the influence of factors such as vibration, evaporation, surface tension change and the like, the object to be measured in the measuring process is difficult to keep still, and the change of the object to be measured in a measuring point is unpredictable, so that unpredictable errors are brought to measurement. In order to solve the problems, in the prior art, a program-controlled high-precision three-dimensional displacement table is adopted to drive a Raman probe to realize accurate position scanning, but the problem of focusing can be only partially solved, and the problems of long focusing time and movement of a target to be measured after focusing can not be solved. And the program-controlled high-precision three-dimensional displacement platform has a complex structure, is expensive, has a volume which is dozens of times or even hundreds of times larger than that of the Raman probe, and brings inconvenience to the application.
Disclosure of Invention
The invention aims to solve the problems in the prior art and provides a rapid Raman scanning imager to solve the problems of time extension caused by repeated focusing and unpredictable measurement signal errors caused by displacement of a measurement point after focusing is finished.
The invention adopts the following technical scheme to solve the technical problems
The structure of the rapid Raman scanning imager is characterized in that:
the imaging instrument comprises a spectrometer, a laser, a light excitation and acquisition module and a detachable Raman enhancement substrate, wherein the Raman enhancement substrate is arranged on a focal plane of a scanning field lens in the light excitation and acquisition module, and an object to be measured is attached to the Raman enhancement substrate, so that the object to be measured is coupled with a nano enhancement microstructure in the Raman enhancement substrate to form a complex and is fixed; the optical excitation and collection module comprises an excitation light path and a collection light path;
the excitation light path is as follows: the method comprises the following steps that emergent light of a laser is guided into an excitation optical fiber collimating mirror by excitation optical fibers to be collimated into parallel light beams, the parallel light beams reach a scanning galvanometer through a low-pass dichroic mirror, then are projected to a reflecting mirror through the scanning galvanometer, enter a scanning field lens after being reflected by the reflecting mirror, form a focus light spot on a focal plane of the scanning field lens, and act with an object to be detected on a Raman enhancement substrate to generate Raman scattering light;
the collection light path: the Raman scattered light mixed stray light and part of light emitted by a laser jointly form collimated light beams through a scanning field lens, the collimated light beams are reflected by a reflector and then reach a low-pass dichroic mirror through a scanning vibrating mirror, then are reflected by the low-pass dichroic mirror and then reach a notch filter through the signal light reflector, and are projected to a low-pass side pass filter through the notch filter, collected light beams are obtained after passing through the low-pass side pass filter, the collected light beams are converged by an optical fiber collimating mirror and then are guided into a collecting optical fiber, and the collected light beams enter a spectrometer through the collecting optical fiber, and the Raman spectrum of an object to be measured is formed by the spectrometer;
and controlling the scanning galvanometer to scan according to a set scanning track, so that a focus light spot formed on a focal plane of the scanning field lens traverses and scans the surface of the joint position of the object to be detected and the Raman enhancement substrate according to the set scanning track, simultaneously acquiring a Raman spectrum of each scanning point in the scanning process from a spectrometer, arranging the Raman spectrum of each scanning point according to the scanning sequence to form a Raman spectrum array, further acquiring a Raman image of the object to be detected, and realizing rapid Raman scanning imaging.
The structure of the rapid Raman scanning imager is also characterized in that: and an excitation light band-pass filter is arranged between the excitation optical fiber collimating mirror and the low-pass dichroic mirror and is used for filtering light with the wavelength beyond the central wavelength lambda +/-0.01 nm of the light emitted by the laser, which is mixed in before the parallel light beam enters the excitation light band-pass filter.
The structure of the rapid Raman scanning imager is also characterized in that: the notch filter is used for filtering out part of contained light emitted by the laser; the low-pass side-pass filter is used for filtering stray light.
The structure of the rapid Raman scanning imager is also characterized in that: the device comprises a support and protection cover, a light excitation and collection module, a spectrometer and a laser, wherein the light excitation and collection module is arranged inside the support and protection cover; the Raman enhancement substrate is fixed on the corresponding position of the support and the protective cover through a Raman enhancement substrate fixing ring and is superposed with the focal plane of a scanning field lens in the optical excitation and acquisition module.
The structure of the rapid Raman scanning imager is also characterized in that: the Raman enhancement substrate takes a latticed base material as a framework, and the nanometer enhancement microstructure for enhancing the Raman signal intensity is attached to the framework to form the three-dimensional reticular enhancement substrate.
The structure of the rapid Raman scanning imager is also characterized in that: the Raman enhancement substrate is arranged to be a basin-shaped structure with a flat bottom and a basin edge, and the Raman enhancement substrate is fixed on the port of the support and protection cover by the aid of the basin edge through the fixing ring, so that the Raman enhancement substrate is fixed.
The structure of the rapid Raman scanning imager of the invention is also characterized in that: a protective optical filter is arranged between the scanning field lens and the Raman enhancement substrate in the support and the protective cover, and the protective optical filter is a band-pass optical filter; the parameters of each device are set to meet the following requirements:
A-B=λ-D;B-λ≥4000cm -1 ;E=A+B;F=λ;G≥D;H=B;
i = G; j is more than or equal to K; l is more than or equal to lambda +5nm and less than or equal to lambda +25nm; wherein:
a is the central wavelength of the protective filter; b is the half-wave peak width of the protective filter;
λ is the central wavelength of the laser emitted by the laser; d is the half-wave peak width of the laser emitted by the laser;
cm -1 is in units of wave number; e is the cut-off wavelength of the low-pass side-pass filter;
f is the central wavelength of the notch filter; g is the half-wave peak width of the notch filter;
h is the working bandwidth of the scanning field lens; i is the half-wave peak width of the band-pass filter;
j is the working angle of the scanning galvanometer; k is the working angle of the scanning field lens;
l is the cut-off wavelength of the low-pass dichroic mirror.
Compared with the prior art, the invention has the beneficial effects that:
1. the method and the device realize the scanning of the surface of the substance to be detected without any focusing operation, greatly shorten the time of Raman point scanning imaging of the surface of the substance, and are particularly suitable for being applied to the technical field of accurate substance identification of the surface of the substance.
2. The invention utilizes the three-dimensional mesh enhanced substrate of the Raman enhanced substrate to adsorb the object to be measured with fluidity or micro-particle shape on the provided three-dimensional mesh enhanced substrate and fix the object to be measured on the focal plane of the scanning field lens, and limits the micro displacement of the point to be measured in the measuring process within the range of 10um, thereby greatly reducing the measuring error of the Raman signal.
3. The invention does not need to focus on each measuring point in the scanning process, thereby saving the measuring time, reducing the precision displacement system required by focusing and greatly reducing the complexity of the system.
Drawings
FIG. 1 is a schematic diagram of an imager system according to the present invention;
reference numbers in the figures: the optical fiber Raman spectrometer comprises a spectrometer 1, a laser 2, a support and protective cover 3, a light excitation and collection module 4, a collection optical fiber 401, a collection optical fiber collimating mirror 402, a low-pass side-pass optical filter 403, a notch optical filter 404, a signal light reflecting mirror 405, a reflecting mirror 406, a scanning field lens 407, a protective optical filter 408, an excitation optical fiber 409, an excitation optical fiber collimating mirror 410, a band-pass optical filter 411, a low-pass dichroic mirror 412, a scanning galvanometer 413, a fixing ring 5 and a Raman enhancement substrate 6.
Detailed Description
Referring to fig. 1, the fast raman scanning imager in this embodiment includes a spectrometer 1, a laser 2, a light excitation and collection module 4, and a detachable raman enhancement substrate 6, where the raman enhancement substrate 6 is disposed on a focal plane of a scanning field lens 407 in the light excitation and collection module 4, and an object to be measured is attached to the raman enhancement substrate 6, so that the object to be measured and a nano enhancement microstructure in the raman enhancement substrate 6 are coupled to form a complex and are fixed accordingly; the optical excitation and collection module 4 includes an excitation optical path and a collection optical path.
In the excitation light path shown in fig. 1, the exit light of the laser 2 is guided into the excitation fiber collimator 410 by the excitation fiber 409 and collimated into parallel light beams, the parallel light beams reach the scanning galvanometer 413 through the low-pass dichroic mirror 412, then are projected to the reflecting mirror 406 through the scanning galvanometer 413, enter the scanning field lens 407 after being reflected by the reflecting mirror 406, form a focal spot on the focal plane of the scanning field lens 407, and generate raman scattering light by the action with the object to be detected on the raman-enhanced substrate 6.
In the collecting light path shown in fig. 1, the raman scattering light mixed stray light and part of light emitted by the laser 2 are formed into a collimated light beam by the scanning field lens 407, the collimated light beam is reflected by the reflector 406 and then reflected by the scanning vibration lens 413 to the low-pass dichroic mirror 412, and then reflected by the low-pass dichroic mirror 412 to the signal light reflecting mirror 405, reflected by the signal light reflecting mirror 405 to the notch filter 404, and projected to the low-pass side-pass filter 403 through the notch filter 404, so as to obtain a collected light beam, the collected light beam is converged by the fiber collimator mirror 402 and then guided to the collecting fiber 401, and enters the spectrometer 1 through the collecting fiber 401, and a raman spectrum of an object to be measured is formed by the spectrometer 1.
In specific implementation, the scanning galvanometer 413 is controlled to scan according to a set scanning track, so that a focal spot formed on a focal plane of the scanning field lens 407 traverses and scans the surface of the joint position of the object to be detected and the raman enhancement substrate 6 according to the set scanning track, simultaneously a raman spectrum of each scanning point in the scanning process is obtained from the spectrometer 1, the raman spectra of each scanning point are arranged according to the scanning sequence to form a raman spectrum array, a raman image of the object to be detected is obtained, and rapid raman scanning imaging is realized.
In one embodiment, the scan field lens 407 may be a scan lens, an F-Theta scan lens, or other optical structure that ensures that the focal point always falls on the focal plane when parallel light is incident at an angle to the optical axis.
The invention avoids the process of focusing once when changing a sampling point each time in the traditional point scanning mode by fixing the Raman enhancement substrate 6 on the focal plane of the scanning field lens 407 in the optical excitation and acquisition module 4, which brings two advantages: firstly, time is saved, and the scanning time can be greatly reduced because each sampling point is not required to be focused, so that the adaptability of the scanning process to some samples (such as living biological samples, easily oxidized samples and the like) which change rapidly along with time is stronger; secondly, a focusing structure or a module and an algorithm in the traditional mode are avoided, the signal intensity of a Raman signal is greatly influenced by the distance between a point to be measured and a focus in the Raman measurement process of a single point (including single-point scanning and single-point measurement), and the Raman signal change can reach 10% when the point to be measured moves 0.125mm relative to the focal plane, so that a precise displacement control module or a structure is needed to ensure the displacement precision, and a rapid displacement control system and an algorithm are needed to accelerate the focusing process.
In specific implementation, the corresponding technical measures also include:
an excitation light band-pass filter 411 is arranged between the excitation fiber collimating mirror 410 and the low-pass dichroic mirror 412, and the excitation light band-pass filter 411 is used for filtering out light with a wavelength beyond the optical center wavelength λ ± 0.01nm emitted by the laser 2, mixed in by the parallel light beams before entering the excitation light band-pass filter 411.
The notch filter 404 is used to filter out the included part of the light emitted by the laser 2; the low-pass side-pass filter 403 is used to filter out stray light.
A support and protection cover 3 is arranged, a light excitation and collection module 4 is arranged inside the support and protection cover 3, and a spectrometer 1 and a laser 2 are arranged outside the support and protection part 3; the Raman enhancement substrate 6 is fixed on the corresponding position of the support and protection cover 3 through a Raman enhancement substrate fixing ring 5 and is superposed with the focal plane of a scanning field lens 407 in the optical excitation and acquisition module 4; the support and shield 3, optical excitation and collection module 4, retaining ring 5, raman-enhanced substrate 6 may be integrated as a probe portion and separated from the spectrometer 1 and laser 2 and connected by an elongated collection fiber 401 and excitation fiber 409. The probe part can be hung on a follow-up mechanical arm for scanning, or the scanning can be completed in a handheld mode. During scanning, the Raman enhancement substrate 6 of the probe part needs to be in full contact with the surface to be detected, and relative displacement between the two is not required before scanning is finished.
A protective filter 408 is arranged between the scanning field lens 407 and the Raman enhancement substrate 6 in the support and shield 3, and the protective filter 408 is a band-pass filter; the parameters of each device are set to meet the following requirements:
A-B=λ-D;B-λ≥4000cm -1 ;E=A+B;F=λ;G≥D;H=B;
i = G; j is more than or equal to K; l is more than or equal to lambda +5nm and less than or equal to lambda +25nm; wherein:
a is the center wavelength of the protective filter 408; b is the half-wave peak width of the protective filter 408;
λ is the central wavelength of the laser light emitted by the laser 2; d is the half-wave peak width of the laser emitted by the laser 2;
cm -1 is in units of wave number; e is the cut-off wavelength of the low-pass side-pass filter 403;
f is the center wavelength of the notch filter 404; g is the half-wave peak width of the notch filter 404;
h is the operating bandwidth of the scan field lens 407; i is the half-wave peak width of the band pass filter 411;
j is the working angle of the scanning galvanometer 413; k is the working angle of the scanning field lens 407;
l is the cut-off wavelength of the low-pass dichroic mirror 412.
In this embodiment, the raman-enhanced substrate 6 is a three-dimensional network-enhanced substrate formed by attaching a nano-enhanced microstructure for enhancing raman signal intensity to a lattice-shaped base material as a framework; the Raman enhancement substrate 6 is arranged to be a basin-shaped structure with a flat bottom and a basin edge, and the Raman enhancement substrate is fixed on the port of the support and protection cover 3 by the aid of the basin edge through the fixing ring 5, so that the Raman enhancement substrate 6 is fixed.
In specific implementation, the latticed base material of the raman enhancement substrate 6 is a copper net, an aluminum net or a silver net, which has high mechanical strength and plasticity, and the nano enhancement microstructure is nano silver, nano gold, nano graphene or other materials with raman enhancement effect.
The nano-enhanced microstructure has a strong capillary phenomenon, when in measurement, the Raman enhanced substrate 6 is tightly attached to a sample to be measured, and the surface part of the sample to be measured is absorbed into the Raman enhanced substrate 6 to form a tightly coupled complex with the nano-enhanced microstructure, so that a measured object is effectively fixed, and the measured point of the measured object cannot generate obvious displacement in the measurement process; when laser light is irradiated to the composite, the raman signal can be increased by several orders of magnitude due to the micro surface plasmon phenomenon, and the form is maintained until the end of scanning when the micro voids in the raman enhancing substrate 6 are filled. According to the grid size of the grid-shaped base material of the Raman enhancement substrate 6, the displacement of a point to be measured can be generally limited to be below 10 mu m, and for some objects to be measured with fluidity, such as powder, colloidal objects and liquid, the stability of Raman signals in the measuring process can be ensured.
As for the three-dimensional mesh-like reinforcing substrate, there is disclosed in document 1 a three-dimensional mesh-like reinforcing substrate, document 1 having DOI format https:// doi.org/10.1016/j.carbon.2018.03.050 (which is DOI format that is one of international reference formats), which describes that a nano reinforcing microstructure for reinforcing raman signal strength is attached to a skeleton to form a three-dimensional mesh-like reinforcing substrate with a woven mesh-like base material as the skeleton; the latticed base material can adopt a structural form corresponding to that recorded in the document 1, or can be formed into a grid by punching holes arranged in rows and columns or in a radial arrangement mode on a base material plate, wherein the grid can be a circular hole or a square hole, and for the circular hole grid, the maximum grid pore diameter is required to be less than 0.15mm; for square hole grids, the minimum grid density of the square hole grids is 200 meshes. Meanwhile, in order to reliably realize the capillary phenomenon, a single grid is taken as an object, and the coverage area of the nano reinforced microstructure aiming at the single grid is required to be set to be not less than 1/2 of the area of the single grid.
While particular embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that changes may be made in these embodiments without departing from the principles of the invention, the scope of which is defined in the appended claims and their equivalents.

Claims (6)

1. A fast Raman scanning imager is characterized in that:
the imaging instrument comprises a spectrometer (1), a laser (2), a light excitation and collection module (4) and a detachable Raman enhancement substrate (6), wherein the Raman enhancement substrate (6) is arranged on a focal plane of a scanning field lens (407) in the light excitation and collection module (4), and an object to be detected is attached to the Raman enhancement substrate (6) so that the object to be detected and a nano enhancement microstructure in the Raman enhancement substrate (6) are coupled to form a complex and are fixed; the optical excitation and collection module (4) comprises an excitation light path and a collection light path;
the excitation light path is as follows: the method comprises the steps that emergent light of a laser (2) is guided into an excitation fiber collimating mirror (410) through excitation fibers and collimated into parallel light beams, the parallel light beams penetrate through a low-pass dichroic mirror (412) to reach a scanning vibrating mirror (413), then are projected to a reflecting mirror (406) through the scanning vibrating mirror (413), are reflected by the reflecting mirror (406) and then enter a scanning field lens (407), focus light spots are formed on a focal plane of the scanning field lens (407), and Raman scattering light is generated on a Raman enhancement substrate (6) under the action of an object to be detected;
the collection light path: the Raman scattered light mixed stray light and part of light emitted by a laser (2) form collimated light beams through a scanning field lens (407), the collimated light beams are reflected by a reflecting mirror (406) and then reflected by a scanning vibrating mirror (413) to a low-pass dichroic mirror (412), the collimated light beams are reflected by the low-pass dichroic mirror (412) to a signal light reflecting mirror (405), reflected by the signal light reflecting mirror (405) to a notch filter (404), transmitted by the notch filter (404) to a low-pass filter (403), collected light beams are obtained through the low-pass filter (403), the collected light beams are converged by a fiber collimating mirror (402) and then guided into a collecting optical fiber (401), and enter a spectrometer (1) through the collecting optical fiber (401), and a Raman spectrum of an object to be measured is formed by the spectrometer (1);
and controlling the scanning galvanometer (413) to scan according to a set scanning track, so that a focus light spot formed on a focal plane of the scanning field lens (407) traverses and scans the surface of the joint position of the object to be detected and the Raman enhancement substrate (6) according to the set scanning track, simultaneously obtaining a Raman spectrum of each scanning point in the scanning process from the spectrometer (1), arranging the Raman spectrum of each scanning point according to the scanning sequence to form a Raman spectrum array, further obtaining a Raman image of the object to be detected, and realizing rapid Raman scanning imaging.
2. The fast raman scan imager of claim 1, wherein: an excitation light band-pass filter (411) is arranged between the excitation fiber collimating mirror (410) and the low-pass dichroic mirror (412), and the excitation light band-pass filter (411) is used for filtering light with a wavelength beyond the central wavelength lambda +/-0.01 nm of the light emitted by the laser (2) mixed in before the parallel light beams enter the excitation light band-pass filter (411).
3. The fast raman scan imager of claim 1, wherein: the notch filter (404) is used for filtering out the contained part of light emitted by the laser (2); the low-pass side-pass filter (403) is used for filtering stray light.
4. The fast raman scan imager of claim 1, wherein: a support and protection cover (3) is arranged, the light excitation and collection module (4) is arranged inside the support and protection cover (3), and the spectrometer (1) and the laser (2) are arranged outside the support and protection cover (3); the Raman enhancement substrate (6) is fixed on the corresponding position of the support and the protective cover (3) through a Raman enhancement substrate fixing ring (5) and is superposed with the focal plane of a scanning field lens (407) in the optical excitation and acquisition module (4).
5. The fast raman scan imager of claim 1, wherein: the Raman enhancement substrate (6) takes a latticed base material as a framework, and the nano enhancement microstructure for enhancing the Raman signal intensity is attached to the framework to form a three-dimensional reticular enhancement substrate.
6. The fast raman scan imager of claim 4, wherein: a protective filter (408) is arranged between the scanning field lens (407) and the Raman enhancement substrate (6) in the support and protection cover (3), and the protective filter (408) is a band-pass filter; the parameters of each device are set to meet the following requirements:
A-B=λ-D;B-λ≥4000cm -1 ;E=A+B;F=λ;G≥D;H=B;
i = G; j is more than or equal to K; l is more than or equal to lambda +5nm and less than or equal to lambda +25nm; wherein:
a is the central wavelength of the protective filter (408); b is the half-wave peak width of the protective filter (408);
lambda is the central wavelength of the laser emitted by the laser (2); d is the half-wave peak width of the laser emitted by the laser (2);
cm -1 is in wave number units; e is the cut-off wavelength of the low-pass side-pass filter (403);
f is the center wavelength of the notch filter (404); g is a half-wave peak width of the notch filter (404);
h is the working bandwidth of the scanning field lens (407); i is the half-wave peak width of the band-pass filter (411);
j is the working angle of the scanning galvanometer (413); k is the working angle of the scanning field lens (407);
l is the cut-off wavelength of the low-pass dichroic mirror (412).
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