Method and system for constructing two-dimensional spectrum reduction model of echelle grating spectrometer

Abstract

Method and system for constructing two-dimensional spectrum reduction model of echelle grating spectrometer, belonging to the technical field of two-dimensional spectrum reduction of echelle grating spectrometer, solves the problem that the existing spectrum reduction model of echelle grating spectrometer shows large errors in the detection range of inflatable wide-band spectrum. Establish the relationship between the wavelength in the Y direction of echelle grating diffraction and the position of detector pixels; establish the relationship between the wavelength in the X direction of prism dispersion and the position of detector pixels; based on the established relationship between the wavelength in the Y direction of echelle grating diffraction and the position of detector pixels, and the established relationship between the wavelength in the X direction of prism dispersion and the position of detector pixels, construct a two-dimensional spectrum reduction model of echelle grating spectrometer; calibrate the two-dimensional spectrum reduction model of echelle grating spectrometer based on a standard light source, optimize the optical structure parameters in the two-dimensional spectrum reduction model, and obtain the optimal two-dimensional spectrum reduction model of echelle grating spectrometer.

Description

Technical Field

[0001] The present invention relates to the technical field of two-dimensional spectrum reduction of echelle spectrometers, and particularly to a method and a system for constructing a two-dimensional spectrum reduction model of an echelle spectrometer. Background Art

[0002] Spectral analysis, as an indispensable means in scientific research, with the continuous progress of technology, has increasingly higher requirements for its spectral coverage range, resolution, measurement accuracy and other performance. Especially in the far ultraviolet band, it is of great significance for exploring the microscopic structure of substances, analyzing environmental pollutants, observing biological reaction mechanisms, etc. The echelle spectrometer has the advantages of wide spectral range, high spectral resolution, high energy efficiency, small volume, etc., and can obtain spectral images of the entire spectral band through a single measurement. It is the preferred spectroscopic instrument for advanced spectral analysis systems such as laser-induced plasma spectroscopy, microwave plasma torch, inductively coupled plasma atomic emission spectroscopy, etc.

[0003] The traditional design of echelle spectrometers mainly targets the near ultraviolet band, visible light band, infrared band, etc., and the spectra in this range can all propagate in the air. When the detection range of the spectrometer covers the far ultraviolet band, due to the strong absorption of ultraviolet spectra by substances such as water vapor, oxygen, and carbon dioxide in the air, it greatly limits the transmission efficiency and signal-to-noise ratio of spectral signals, making it impossible for the detector to detect far ultraviolet spectra. To solve this problem, inert gases are started to be used as the spectral transmission medium during the development of echelle spectrometers. Inert gases have low absorption and stable chemical properties in the far ultraviolet band and are an ideal choice for far ultraviolet spectral transmission media.

[0004] Different from spectrometers in the traditional atmospheric environment, when the spectrometer is filled with inert gas, although the transmission efficiency of spectral signals is improved, it inevitably causes a change in the light transmission medium, which directly affects the optical imaging quality and resolution of the spectrometer. The change in the light transmission medium will cause the spectral imaging position to shift, thereby reducing the accuracy and reliability of the spectrum reduction of the echelle spectrometer. In addition, the traditional spectrum reduction model of the echelle spectrometer is often designed based on air medium and relies on a simplified optical design model, ignoring the changes in complex optical design structures and the refractive index of the transmission medium, which directly leads to large errors in the detection range of the inflated wide-band spectrum.

[0005] In summary, the existing spectrum reduction model of the echelle spectrometer ignores the changes in complex optical design structures and the refractive index of the transmission medium, which directly leads to large errors in the detection range of the inflated wide-band spectrum. Summary of the Invention

[0006] The present invention solves the problem that the existing echelle grating spectrometer spectral reduction model exhibits large errors within the detection range of an inflated wide-band spectrum.

[0007] The method for constructing an echelle grating spectrometer two-dimensional spectral reduction model according to the present invention includes the following steps:

[0008] Step S1, based on the principles of geometric optics and considering the change in the refractive index of the medium through which the light passes, establish the relationship between the wavelength in the Y direction of echelle grating diffraction and the pixel position of the detector;

[0009] Step S2, based on the principles of geometric optics and considering the change in the refractive index of the medium through which the light passes, establish the relationship between the wavelength in the X direction of prism dispersion and the pixel position of the detector;

[0010] Step S3, based on the established relationship between the wavelength in the Y direction of echelle grating diffraction and the pixel position of the detector, and the established relationship between the wavelength in the X direction of prism dispersion and the pixel position of the detector, construct an echelle grating spectrometer two-dimensional spectral reduction model;

[0011] Step S4, calibrate the echelle grating spectrometer two-dimensional spectral reduction model based on a standard light source, optimize the optical structure parameters in the two-dimensional spectral reduction model, and obtain the optimal echelle grating spectrometer two-dimensional spectral reduction model.

[0012] Further, in an embodiment of the present invention, in step S1, the consideration of the change in the refractive index of the medium through which the light passes is to introduce the refractive index parameter of the gas medium through which the light is transmitted.

[0013] Further, in an embodiment of the present invention, in step S1, the establishment of the relationship between the wavelength in the Y direction of echelle grating diffraction and the pixel position of the detector is specifically as follows:

[0014] When establishing the echelle grating spectrometer two-dimensional spectral reduction model in the Y direction of echelle grating diffraction, based on the incident light wavelength in the Y direction of echelle grating diffraction, calculate the offset of the light by the correction lens provided between the focusing lens and the detector, and obtain the offset of the light in the Y direction of the detector.

[0015] Further, in an embodiment of the present invention, the offset of the light in the Y direction of the detector is specifically as follows:

[0016] ;

[0017] Among them, is the offset of the light in the Y direction of the detector, is the distance from the intersection point of the light passing through the correction lens and the rear surface to the intersection point of the optical axis, is the distance from the rear surface of the correction lens to the detector, is the angle between the light ray and the optical axis.

[0018] Further, in an embodiment of the present invention, in step S2, the establishment of the relationship between the prism dispersion X-direction wavelength and the detector pixel position is specifically as follows:

[0019] When establishing a two-dimensional spectrum reduction model of an echelle spectrometer in the prism dispersion X direction, based on the incident light wavelength in the prism dispersion X direction, calculate the offset of the light ray by the correction lens provided between the focusing lens and the detector, and obtain the offset of the light ray in the detector X direction.

[0020] Further, in an embodiment of the present invention, the offset of the light ray in the detector X direction is specifically as follows:

[0021] ;

[0022] Wherein, is the offset of the light ray in the detector X direction, is the distance from the intersection point of the light ray passing through the correction lens and the rear surface to the intersection point of the optical axis, is the distance from the focusing lens to the front surface of the correction lens, is the thickness of the correction lens, is the distance from the rear surface of the correction lens to the detector, is the distance from the intersection point of the light ray passing through the front surface of the correction lens and the optical axis to the center of the focusing lens, is the distance from the intersection point of the light ray passing through the front surface of the correction lens and the optical axis to the intersection point of the light ray passing through the rear surface of the correction lens and the optical axis, is the angle between the light ray and the optical axis.

[0023] Further, in an embodiment of the present invention, if the correction lens includes multiple lens groups, the offset of the light ray in the detector Y direction is specifically as follows:

[0024] ;

[0025] Wherein, is that the correction lens includes multiple lens groups, and the offset of the light ray in the detector Y direction, is the distance between the light ray in the Y direction and the center of the focusing lens, , , , , , and are all the offsets of the light ray in the Y direction. The media and correction lens parameters passed by the light ray in the Y direction are different, and the offsets are also different. and are all positive integers, and and not equal to 1, 2, 3, 4, and 5, ≠ ;

[0026] then the offset of the light in the X direction of the detector is specifically:

[0027] ;

[0028] wherein, the correction lens includes multiple lens groups, and the offset of the light in the X direction of the detector, the distance between the light in the X direction and the center of the focusing lens, , , , , , and are all the offsets of the light in the X direction. The offsets are different because the media passed by the light in the X direction and the parameters of the correction lens are different.

[0029] Furthermore, in an embodiment of the present invention, when solving the , , , , , , , , , , , , and geometric optical principles are adopted and the change of the refractive index of the media passed by the light is considered.

[0030] Furthermore, in an embodiment of the present invention, for step S4 of calibrating the two-dimensional spectral reduction model of the echelle spectrometer based on a standard light source and optimizing the optical structure parameters in the two-dimensional spectral reduction model, the following steps are included:

[0031] Step S401, obtaining the initial optical structure parameters in the constructed two-dimensional spectral reduction model of the echelle spectrometer;

[0032] The optical structure parameters in the constructed two-dimensional spectral reduction model of the echelle spectrometer include the refractive index of the medium, the grating incident angle, the prism apex angle, the grating offset angle, and the system focal length;

[0033] Step S402, traversing the optical structure parameters in the constructed two-dimensional spectral reduction model of the echelle spectrometer and generating the fitting coordinate positions of the two-dimensional spectral reduction model of the echelle spectrometer;

[0034] Step S403: Based on the characteristic wavelengths of the standard light source, calculate the sum of the mean square errors between the fitting coordinate positions and the actual coordinate positions of the two-dimensional spectral reduction model of the echelle spectrometer respectively.

[0035] Step S404: Determine whether the sum of the mean square errors reaches the minimum. If so, execute Step S405; if not, return to Step S402.

[0036] Step S405: Complete the calibration and optimization of the optical structure parameters in the constructed two-dimensional spectral reduction model of the echelle spectrometer.

[0037] The system for constructing the two-dimensional spectral reduction model of the echelle spectrometer according to the present invention includes the following modules:

[0038] The first establishment module: Based on the geometric optical principle and considering the change in the refractive index of the medium through which the light passes, establish the relationship between the wavelength in the Y direction of the echelle diffraction and the position of the detector pixel.

[0039] The second establishment module: Based on the geometric optical principle and considering the change in the refractive index of the medium through which the light passes, establish the relationship between the wavelength in the X direction of the prism dispersion and the position of the detector pixel.

[0040] The construction module: Based on the established relationship between the wavelength in the Y direction of the echelle diffraction and the position of the detector pixel, and the established relationship between the wavelength in the X direction of the prism dispersion and the position of the detector pixel, construct the two-dimensional spectral reduction model of the echelle spectrometer.

[0041] The calibration and optimization module: Calibrate the two-dimensional spectral reduction model of the echelle spectrometer based on the standard light source, optimize the optical structure parameters in the two-dimensional spectral reduction model, and obtain the optimal two-dimensional spectral reduction model of the echelle spectrometer.

[0042] The present invention solves the problem that the existing spectral reduction model of the echelle spectrometer shows large errors in the inflatable wide-band spectral detection range. The specific beneficial effects include:

[0043] 1. For the method of constructing the two-dimensional spectral reduction model of the echelle spectrometer according to the present invention, the present invention adopts the mathematical modeling method, calculates the light transmission path and imaging position through the geometric optical principle, constructs the mapping relationship between the wavelength and the coordinate position of the detector pixel, and realizes the accurate conversion of the spectrum, thereby solving the problem that the existing spectral reduction model of the echelle spectrometer shows large errors in the inflatable wide-band spectral detection range.

[0044] 2. The method for constructing a two-dimensional spectral map reduction model of an echelle grating spectrometer according to the present invention performs geometric optical calculations when constructing the two-dimensional spectral map reduction model of the echelle grating spectrometer, fully considering the change in the refractive index of the light transmission medium, ensuring the accuracy of the imaging position calculation, and thus solving the problem in the prior art that the filling of inert gas has a significant impact on the refractive index of the internal medium of the echelle grating spectrometer;

[0045] 3. The method for constructing a two-dimensional spectral map reduction model of an echelle grating spectrometer according to the present invention corrects the constructed two-dimensional spectral map reduction model of the echelle grating spectrometer, and optimizes the parameters of the refractive index of the medium, the grating incident angle, the prism apex angle, the grating offset angle, and the system focal length in the constructed two-dimensional spectral map reduction model of the echelle grating spectrometer, thereby improving the accuracy and reliability of the two-dimensional spectral map reduction model of the echelle grating spectrometer;

[0046] 4. The method for constructing a two-dimensional spectral map reduction model of an echelle grating spectrometer according to the present invention improves the accuracy of the two-dimensional spectral map reduction model of the echelle grating spectrometer by accurately analyzing the complex influence of the correction lens on the light transmission path;

[0047] The method for constructing a two-dimensional spectral map reduction model of an echelle grating spectrometer according to the present invention is used for the reduction of the two-dimensional spectral map of an inflated wide-band echelle grating spectrometer with a spectral range covering the far ultraviolet band. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] The above and / or additional aspects and advantages of the present invention will become apparent and easy to understand from the following description of the embodiments in conjunction with the drawings, where:

[0049] Figure 1 is a diagram showing the offset relationship in the Y direction of diffraction of the echelle grating between the focusing mirror and the correction lens in Embodiment 1;

[0050] Figure 2 is a diagram showing the offset relationship in the X direction of prism dispersion between the focusing mirror and the correction lens in Embodiment 1;

[0051] Figure 3 is a diagram of the constructed two-dimensional spectral map reduction model of the echelle grating spectrometer in Embodiment 1;

[0052] Figure 4 is a result diagram of the unoptimized optical structure parameters in the two-dimensional spectral map reduction model of the echelle grating spectrometer in Embodiment 3;

[0053] Figure 5 is a result diagram of the optimized optical structure parameters in the two-dimensional spectral map reduction model of the echelle grating spectrometer in Embodiment 3. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0054] The following will clearly and completely describe various embodiments of the present invention in conjunction with the accompanying drawings. The embodiments described by referring to the accompanying drawings are exemplary and are intended to explain the present invention, but should not be construed as limiting the present invention.

[0055] Embodiment 1. The method for constructing a two-dimensional spectrum reduction model of an echelle grating spectrometer includes the following steps:

[0056] Step S1, based on the principles of geometric optics and considering the change in the refractive index of the medium through which the light passes, establish the relationship between the wavelength in the Y direction of the echelle grating diffraction and the position of the detector pixel;

[0057] Step S2, based on the principles of geometric optics and considering the change in the refractive index of the medium through which the light passes, establish the relationship between the wavelength in the X direction of the prism dispersion and the position of the detector pixel;

[0058] Step S3, based on the established relationship between the wavelength in the Y direction of the echelle grating diffraction and the position of the detector pixel, and the established relationship between the wavelength in the X direction of the prism dispersion and the position of the detector pixel, construct a two-dimensional spectrum reduction model of the echelle grating spectrometer;

[0059] Step S4, calibrate the two-dimensional spectrum reduction model of the echelle grating spectrometer based on a standard light source, optimize the optical structure parameters in the two-dimensional spectrum reduction model, and obtain the optimal two-dimensional spectrum reduction model of the echelle grating spectrometer.

[0060] In this embodiment, in step S1, the consideration of the change in the refractive index of the medium through which the light passes is to introduce the refractive index parameter of the gas medium through which the light is transmitted.

[0061] In this embodiment, in step S1, the establishment of the relationship between the wavelength in the Y direction of the echelle grating diffraction and the position of the detector pixel is specifically as follows:

[0062] When establishing a two-dimensional spectrum reduction model of an echelle grating spectrometer in the Y direction of the echelle grating diffraction, based on the incident light wavelength in the Y direction of the echelle grating diffraction, calculate the offset of the light by the correction lens provided between the focusing lens and the detector, and obtain the offset of the light in the Y direction of the detector.

[0063] In this embodiment, the offset of the light in the Y direction of the detector is specifically as follows:

[0064] ;

[0065] Among them, is the offset of the light in the Y direction of the detector, is the distance from the intersection point of the light passing through the correction lens and the rear surface to the intersection point of the optical axis, is the distance from the rear surface of the correction lens to the detector, is the angle between the light ray and the optical axis.

[0066] In this embodiment, in step S2, establishing the relationship between the wavelength in the X direction of the prism dispersion and the position of the detector pixel specifically includes:

[0067] When establishing the two-dimensional spectrum reduction model of the echelle spectrometer in the X direction of the prism dispersion, based on the wavelength of the incident light in the X direction of the prism dispersion, calculate the offset of the light ray by the correction lens set between the focusing lens and the detector, and obtain the offset of the light ray in the X direction of the detector.

[0068] In this embodiment, the offset of the light ray in the X direction of the detector specifically is:

[0069] ;

[0070] Wherein, is the offset of the light ray in the X direction of the detector, is the distance from the intersection point of the light ray passing through the correction lens and the rear surface to the intersection point of the optical axis, is the distance from the focusing lens to the front surface of the correction lens, is the thickness of the correction lens, is the distance from the rear surface of the correction lens to the detector, is the distance from the intersection point of the light ray passing through the front surface of the correction lens and the optical axis to the center of the focusing lens, is the distance from the intersection point of the light ray passing through the front surface of the correction lens and the optical axis to the intersection point of the light ray passing through the rear surface of the correction lens and the optical axis, is the angle between the light ray and the optical axis.

[0071] In the prior art, the spectrum reduction model of the echelle spectrometer is often designed based on the air medium and relies on a simplified optical design model, ignoring the complex optical design structure and the change of the refractive index of the light transmission medium, which directly leads to a large error in the inflatable wide-band spectral detection range.

[0072] To solve the above technical problems, this embodiment proposes a method for constructing a two-dimensional spectrum reduction model of an echelle spectrometer, including the following steps:

[0073] Step S1, through the principle of geometric optics and considering the change of the refractive index of the light ray passing through the medium, establish the relationship between the wavelength in the Y direction of the echelle diffraction and the position of the detector pixel, specifically including:

[0074] When establishing the two-dimensional spectrum reduction model of the echelle spectrometer in the Y direction of the echelle diffraction, a correction lens is used between the focusing lens and the detector. This detector is a CCD detector, and the offset relationship between the focusing lens and the correction lens in the Y direction of the echelle diffraction is as Figure 1 shown in the figure, where in the figure, is the center of the front surface of the focusing lens, is the distance between the light ray in the Y direction and the center of the focusing lens, is the distance from the focusing lens to the front surface of the correction lens, is the thickness of the correction lens, is the distance from the rear surface of the correction lens to the detector, and are the radii of curvature of the front and rear surfaces of the correction lens respectively.

[0075] The intersection point of the light ray along the propagation direction and the front surface of the correction lens is , and are the incident angle and the refraction angle of the light ray on the front surface of the correction lens respectively, is the intersection point with the optical axis, The distance of is The distance of is The offset of the light ray in the Y direction is . The intersection point of the light ray passing through the correction lens and the rear surface is , and are the incident angle and the refraction angle of the light ray on the rear surface of the correction lens respectively, is the intersection point with the optical axis, The distance of is The distance of is The offset in the Y direction is . The light ray passes through the medium and reaches the detector target surface, and the offset in the Y direction is The angle between the light ray and the optical axis is Therefore, the actual offset of the light ray in the Y direction can be expressed as:

[0076] ;

[0077] To solve , when the light ray passes through the front surface of the correction lens, a right triangle AY1O1 is constructed with the intersection point of the light ray along the propagation direction and the correction lens. According to the Pythagorean theorem, we have:

[0078] ;

[0079] Among them, ;

[0080] ;

[0081] It can be obtained that The expression is:

[0082] ;

[0083] Therefore, there is ;

[0084] Considering the change of the light transmission medium, is the refractive index of the light transmission medium, is the refractive index of the correction lens. According to the trigonometric function and the refraction law, there is:

[0085] ;

[0086] To solve , when the light passes through the rear surface of the correction lens, a right triangle BY2O2 is also constructed with the intersection point of the light and the rear surface. Let . According to the Pythagorean theorem, it can be obtained that The expression is:

[0087] ;

[0088] Therefore, there is ;

[0089] Similarly, considering the change of the light transmission medium, according to the trigonometric function and the refraction law, there is:

[0090] ;

[0091] Therefore, there is ;

[0092] Therefore, in the Y direction of the echelle grating diffraction, the actual offset of the light can be expressed as:

[0093] ;

[0094] The parameters in the above formula are all functions expressed by the incident light wavelength . Therefore, a one-to-one correspondence relationship between the incident light wavelength and the Y-direction coordinate can be established. In this way, the Y-direction position coordinate of the spectrum on the detector can be solved.

[0095] Step S2: Based on the geometric optics principle and considering the change of the refractive index of the medium through which the light passes, establish the relationship between the X-direction wavelength of the prism dispersion and the position of the detector pixel, specifically:

[0096] When establishing a two-dimensional spectral reduction model of an echelle spectrometer in the prism dispersion X direction, a correction lens is also used between the focusing mirror and the detector. The detector is a CCD detector. The offset relationship between the focusing mirror and the correction lens in the prism dispersion X direction is as Figure 2 shown. In the figure, is the incident position of the spectrum at any wavelength on the focusing mirror, is the center of the front surface of the focusing mirror, is the distance between the light ray and the center of the focusing mirror in the X direction, is the center of the sphere of the focusing mirror, , is the radius of curvature of the focusing mirror, is the image plane, , is the focal length, is the exit point of the light ray on the prism, is the exit angle of the reference wavelength on the prism. Then, the angle ∠QUP between the exit light ray of any wavelength on the prism and the exit light ray of the reference wavelength can be expressed as:

[0097] ;

[0098] is the distance from the focusing mirror to the front surface of the correction lens, is the thickness of the correction lens, is the distance from the rear surface of the correction lens to the detector, and are the radii of curvature of the front and rear surfaces of the correction lens respectively. is the intersection point of the light ray along the propagation direction and the front surface of the correction lens, and are the incident angle and the refraction angle of the light ray on the front surface of the correction lens respectively, is the intersection point with the optical axis, The distance of is The distance of is is the offset of the light ray in the X direction, is the angle between the light ray and the optical axis. is the intersection point of the light ray passing through the correction lens and the rear surface, and are the incident angle and the refraction angle of the light ray on the rear surface of the correction lens respectively, is the intersection point with the optical axis, The distance of is The distance of is is the offset of the light ray in the X direction, is the angle between the light ray and the optical axis. The light ray passes through the medium and reaches the detector target surface. is the offset of the light ray in the X direction. is the angle between the light ray and the optical axis. Therefore, in the X direction, the actual offset of the light ray in the X direction can be expressed as:

[0099] ;

[0100] where ;

[0101] is to solve , when the light ray passes through the front surface of the correction lens, taking the intersection point of the light ray along the propagation direction and the correction lens to construct a right triangle EX1O1. According to the Pythagorean theorem, we have:

[0102] ;

[0103] where ;

[0104] ;

[0105] Let , we can obtain The expression is:

[0106] ;

[0107] So, we have ;

[0108] Considering the change of the light ray transmission medium, according to the trigonometric function and the refraction law, we have is the refractive index of the light ray transmission medium, is the refractive index of the correction lens, we can obtain the following equation:

[0109] ;

[0110] is to solve , when the light ray passes through the back surface of the correction lens, taking the intersection point of the light ray and the back surface to construct a right triangle FX2O2. Let , according to the Pythagorean theorem, we can obtain The expression of

[0111] ;

[0112] So, we have ;

[0113] Similarly, considering the change of the light ray transmission medium, according to the trigonometric function and the refraction law, we have:

[0114] ;

[0115] Therefore, there is which can be expressed as:

[0116] ;

[0117] Therefore, in the prism dispersion direction, the actual offset of the light in the X direction can be expressed as:

[0118] ;

[0119] The parameters in the above formula are all functions expressed by the wavelength of the incident light . Therefore, a one-to-one correspondence relationship between the wavelength of the incident light and the X-direction coordinate can be established, and the X-direction position coordinate of the spectrum on the detector can be solved by this method.

[0120] Step S3: Based on the established relationship between the wavelength in the Y direction of the echelle grating diffraction and the position of the detector pixels, and the established relationship between the wavelength in the X direction of the prism dispersion and the position of the detector pixels, construct a two-dimensional spectrum reduction model of the echelle grating spectrometer;

[0121] Based on the established relationship between the wavelength in the Y direction of the echelle grating diffraction and the position of the detector pixels, and the established relationship between the wavelength in the X direction of the prism dispersion and the position of the detector pixels, they jointly constitute a complete two-dimensional spectrum reduction model of the echelle grating spectrometer.

[0122] Based on the principles of geometric optics, respectively represent the mapping relationships between the wavelength of the incident light and the Y direction and the X direction. For this reason, the correlation matrix between the wavelength of the incident light and the pixels of the detector is expressed as:

[0123] ;

[0124] Among them, , are both the positions of the detector pixels.

[0125] As Figure 3 shown, the number of rows and columns of this matrix respectively correspond to the pixel coordinates on the detector target surface, and each element value in the matrix represents the wavelength value at the corresponding position.

[0126] Step S4: Based on the standard light source, correct and optimize the constructed two-dimensional spectrum reduction model of the echelle grating spectrometer to obtain the optimal two-dimensional spectrum reduction model of the echelle grating spectrometer.

[0127] Therefore, in this embodiment, in order to solve the problems caused by the spectral reduction model of the echelle grating spectrometer often being designed based on an air medium ( ), considering that the detection range of this spectral instrument covers the far ultraviolet band and using a high-pressure inert gas as the spectral transmission medium, when performing geometric optical calculations, the change in the refractive index of the light transmission medium ( ) is fully considered to ensure the accuracy of the imaging position calculation. In addition, in this embodiment, in order to correct the aberration of the optical system, a correction lens is usually designed between the focusing mirror and the detector during the design of the optical system of the spectral instrument. However, since the introduction of the correction lens will lead to a decrease in the accuracy of the imaging position calculation, to solve the above technical problems, this embodiment considers the influence brought by the correction lens, thereby improving the accuracy of the imaging position calculation.

[0128] Embodiment 2: This embodiment further limits the method for constructing the two-dimensional spectral reduction model of the echelle grating spectrometer described in Embodiment 1. If the correction lens includes multiple lens groups, the offset of the light in the Y direction of the detector is specifically:

[0129] ;

[0130] Among them, is the offset of the light in the Y direction of the detector when the correction lens includes multiple lens groups, is the distance between the light in the Y direction and the center of the focusing mirror, , , , , , and are all the offsets of the light in the Y direction. The offsets are different because the media and correction lens parameters that the light passes through in the Y direction are different. and are both positive integers, and and are not equal to 1, 2, 3, 4, and 5, ≠ ;

[0131] Then the offset of the light in the X direction of the detector is specifically:

[0132] ;

[0133] Among them, is the offset of the light in the X direction of the detector when the correction lens includes multiple lens groups, is the distance between the light in the X direction and the center of the focusing mirror, , , , , , and are all the offsets of the light in the X direction. The medium through which the light passes in the X direction and the parameters of the correction lens are different, so the offsets are also different.

[0134] In this embodiment, when solving the , , , , , , , , , , , , and , through the principle of geometric optics and considering the change of the refractive index of the medium through which the light passes.

[0135] The correction lens described in Embodiment 1 is designed to include a lens group. If you want to achieve a better effect in constructing the two-dimensional spectrum reduction model of the echelle grating spectrometer, the correction lens can be designed to include multiple lens groups in the optical design. The specific process of constructing the two-dimensional spectrum reduction model of the echelle grating spectrometer refers to Embodiment 1. Then the correction lens is designed to include two lens groups, and multiple offsets are added when modeling in the X and Y directions respectively. Specifically:

[0136] ;

[0137] ;

[0138] Among them, is the offset when the correction lens is designed to include two lens groups and modeling in the Y direction, is the offset when the correction lens is designed to include two lens groups and modeling in the X direction, is the distance between the light ray and the center of the focusing lens in the Y direction, the distance between the light ray and the center of the focusing lens in the X direction, , , , and are all the offsets of the light in the Y direction. The medium through which the light passes in the Y direction and the parameters of the correction lens are different, so the offsets are also different. , , , and are all the offsets of the light in the X direction. The medium through which the light passes in the X direction and the parameters of the correction lens are different, so the offsets are also different.

[0139] The correction lens is designed to include three lens groups, and multiple offsets are added when modeling in the X and Y directions respectively. Specifically:

[0140] ;

[0141] ;

[0142] Among them, is the offset when modeling in the Y direction for the correction lens designed to include three lens groups, is the offset when modeling in the X direction for the correction lens designed to include three lens groups, , , , , , and are all the offsets of the light in the Y direction. The offsets are different because the media and correction lens parameters that the light passes through in the Y direction are different. , , , , , and are all the offsets of the light in the X direction. The offsets are different because the media and correction lens parameters that the light passes through in the X direction are different.

[0143] Embodiment 3. This embodiment further limits the method for constructing the two-dimensional spectral reduction model of the echelle grating spectrometer described in Embodiment 1. In step S4, based on a standard light source, the two-dimensional spectral reduction model of the echelle grating spectrometer is calibrated to optimize the optical structure parameters in the two-dimensional spectral reduction model, including the following steps:

[0144] Step S401, obtain the initial optical structure parameters in the constructed two-dimensional spectral reduction model of the echelle grating spectrometer;

[0145] The optical structure parameters in the constructed two-dimensional spectral reduction model of the echelle grating spectrometer include the refractive index of the medium, the incident angle of the grating, the apex angle of the prism, the offset angle of the grating, and the system focal length;

[0146] Step S402, traverse the optical structure parameters in the constructed two-dimensional spectral reduction model of the echelle grating spectrometer and generate the fitting coordinate positions of the two-dimensional spectral reduction model of the echelle grating spectrometer;

[0147] Step S403, based on the characteristic wavelength of the standard light source, calculate the sum of the mean square errors between the fitting coordinate positions and the actual coordinate positions of the two-dimensional spectral reduction model of the echelle grating spectrometer;

[0148] Step S404: Determine whether the sum of mean square errors reaches the minimum. If so, execute Step S405; if not, return to Step S402.

[0149] Step S405: Complete the calibration and optimization of the optical structure parameters in the constructed two-dimensional spectral reduction model of the echelle spectrometer.

[0150] In this embodiment, in Step S4, the calibration of the two-dimensional spectral reduction model of the echelle spectrometer based on a standard light source and the optimization of the optical structure parameters in the two-dimensional spectral reduction model include the following steps:

[0151] Step S401: Obtain the initial optical structure parameters in the constructed two-dimensional spectral reduction model of the echelle spectrometer.

[0152] Through the analysis of the geometric relationship between the model imaging position and the detector pixel position, it is determined that the grating incident angle, prism apex angle, grating offset angle, and system focal length are the key factors affecting the accuracy of the two-dimensional spectral reduction model of the echelle spectrometer. At the same time, since this embodiment uses high-pressure inert gas filling as the light transmission medium, the refractive index of the medium inside the instrument changes, and the influence of the refractive index of the medium must be considered in the calibration method. Therefore, these five parameters are selected as the calibration and optimization parameters in this embodiment.

[0153] Step S402: Traverse the optical structure parameters in the constructed two-dimensional spectral reduction model of the echelle spectrometer and generate the fitting coordinate positions of the two-dimensional spectral reduction model of the echelle spectrometer.

[0154] Adopt the method of grid search to sequentially change the input values of the refractive index of the medium, grating incident angle, prism apex angle, grating offset angle, and system focal length, so as to obtain a series of fitting coordinate positions of the two-dimensional spectral reduction model of the echelle spectrometer.

[0155] Step S403: Based on the characteristic wavelength of the standard light source, calculate the sum of mean square errors between the fitting coordinate positions and the actual coordinate positions of the two-dimensional spectral reduction model of the echelle spectrometer respectively.

[0156] By calculating the sum of mean square errors between the fitting coordinate positions and the actual positions of the two-dimensional spectral reduction model of the echelle spectrometer respectively to evaluate the fitness of the model.

[0157] Sum of mean square errors The expression of

[0158] ;

[0159] where is the number of selected characteristic spectra, is the actual abscissa of the characteristic spectrum, is the actual ordinate of the characteristic spectrum, is the calculated abscissa of the characteristic spectrum model, is the calculated ordinate of the characteristic spectrum model.

[0160] Step S404: Determine whether the sum of mean square errors reaches the minimum. If so, execute Step S405; if not, return to Step S402.

[0161] Step S405: Complete the calibration and optimization of the optical structure parameters in the constructed echelle spectrometer two-dimensional spectrum reduction model.

[0162] When the sum of mean square errors reaches the minimum value, the corresponding medium refractive index, grating incident angle, prism apex angle, grating offset angle, and system focal length are the optimal parameters of the echelle spectrometer two-dimensional spectrum reduction model, and thus the optimization of the optical structure parameters is completed.

[0163] Therefore, in this embodiment, by adopting the grid search method, the echelle spectrometer two-dimensional spectrum reduction model is calibrated, and the parameters of the medium refractive index, grating incident angle, prism apex angle, grating offset angle, and system focal length in the echelle spectrometer two-dimensional spectrum reduction model are optimized, thereby improving the accuracy and reliability of the echelle spectrometer two-dimensional spectrum reduction model.

[0164] To better illustrate the method for constructing the echelle spectrometer two-dimensional spectrum reduction model described in this embodiment, it is described in detail through the following embodiments:

[0165] As Figure 4 shown, it is the result of the offset of the characteristic spectrum of the standard light source in the X and Y directions when the optical structure parameters in the echelle spectrometer two-dimensional spectrum reduction model are not optimized. The abscissa is the wavelength with the unit of nm, and the ordinate is the deviation with the unit of pixel. It can be seen that the error in the result of the offset in the X and Y directions is relatively large. As Figure 5 shown, it is the result of the offset of the characteristic spectrum of the standard light source in the X and Y directions when the optical structure parameters in the echelle spectrometer two-dimensional spectrum reduction model have been optimized. The abscissa is the wavelength with the unit of nm, and the ordinate is the deviation with the unit of pixel. It can be seen that the error in the result of the offset in the X and Y directions is significantly reduced.

[0166] Embodiment 4: This embodiment further limits the method for constructing the echelle spectrometer two-dimensional spectrum reduction model described in Embodiment 1, and includes the following modules:

[0167] The first establishment module establishes the relationship between the wavelength in the Y direction of the echelle grating diffraction and the position of the detector pixel through the principles of geometric optics and considering the change in the refractive index of the medium through which the light passes.

[0168] The second establishment module establishes the relationship between the wavelength in the X direction of the prism dispersion and the position of the detector pixel through the principles of geometric optics and considering the change in the refractive index of the medium through which the light passes.

[0169] The construction module constructs a two-dimensional spectrum reduction model of the echelle grating spectrometer based on the established relationship between the wavelength in the Y direction of the echelle grating diffraction and the position of the detector pixel, and the established relationship between the wavelength in the X direction of the prism dispersion and the position of the detector pixel.

[0170] The calibration and optimization module calibrates the two-dimensional spectrum reduction model of the echelle grating spectrometer based on a standard light source, optimizes the optical structure parameters in the two-dimensional spectrum reduction model, and obtains an optimal two-dimensional spectrum reduction model of the echelle grating spectrometer.

[0171] The above has introduced in detail the method and system for constructing a two-dimensional spectrum reduction model of an echelle grating spectrometer. Specific examples are used in this article to elaborate on the principles and implementation manners of the present invention. The description of the above embodiments is only used to help understand the method and its core idea of the present invention; at the same time, for those of ordinary skill in the art, there will be changes in the specific implementation manners and application scopes according to the idea of the present invention. In summary, the content of this specification should not be construed as a limitation to the present invention.

Claims

1. A method for constructing a two-dimensional spectrum reduction model of an echelle grating spectrometer, characterized in that, It includes the following steps: Step S1: Based on the geometric optics principle and considering the refractive index change of the medium through which the light passes, establish the relationship between the wavelength in the Y direction of the echelle grating diffraction and the position of the detector pixels; Step S2: Based on the geometric optics principle and considering the refractive index change of the medium through which the light passes, establish the relationship between the wavelength in the X direction of the prism dispersion and the position of the detector pixels; Step S3: Based on the established relationship between the wavelength in the Y direction of the echelle grating diffraction and the position of the detector pixels, and the established relationship between the wavelength in the X direction of the prism dispersion and the position of the detector pixels, construct a two-dimensional spectrum reduction model for the echelle grating spectrometer; Step S4: Calibrate the two-dimensional spectrum reduction model for the echelle grating spectrometer based on a standard light source, optimize the optical structure parameters in the two-dimensional spectrum reduction model, and obtain the optimal two-dimensional spectrum reduction model for the echelle grating spectrometer.

2. The method for constructing a two-dimensional spectrum reduction model of a echelle grating spectrometer according to claim 1, wherein In the said Step S1, the consideration of the refractive index change of the medium through which the light passes is to introduce the refractive index parameter of the gas medium through which the light travels.

3. The method for constructing a two-dimensional spectrum reduction model of a echelle grating spectrometer according to claim 1, characterized in that, In the said Step S1, the establishment of the relationship between the wavelength in the Y direction of the echelle grating diffraction and the position of the detector pixels is specifically as follows: When establishing the two-dimensional spectrum reduction model for the echelle grating spectrometer in the Y direction of the echelle grating diffraction, based on the wavelength of the incident light in the Y direction of the echelle grating diffraction, calculate the offset of the light by the correction lens set between the focusing lens and the detector, and obtain the offset of the light in the Y direction of the detector.

4. The method for constructing a two-dimensional spectrum reduction model of a echelle grating spectrometer according to claim 3, characterized in that, The offset of the light in the Y direction of the detector is specifically as follows: ； Among them, is the offset of the light in the Y direction of the detector, is the distance from the intersection point of the light passing through the correction lens and the rear surface to the intersection point of the optical axis, is the distance from the rear surface of the correction lens to the detector, is the angle between the light and the optical axis.

5. The method for constructing a two-dimensional spectrum reduction model of a echelle grating spectrometer according to claim 1, wherein In the said Step S2, the establishment of the relationship between the wavelength in the X direction of the prism dispersion and the position of the detector pixels is specifically as follows: When establishing the two-dimensional spectrum reduction model for the echelle grating spectrometer in the X direction of the prism dispersion, based on the wavelength of the incident light in the X direction of the prism dispersion, calculate the offset of the light by the correction lens set between the focusing lens and the detector, and obtain the offset of the light in the X direction of the detector.

6. The method for constructing a two-dimensional spectrum reduction model of a echelle grating spectrometer according to claim 5, wherein The offset of the light in the X direction of the detector is specifically as follows: ； Among them, is the offset of the light in the X direction of the detector, is the distance from the intersection point of the light passing through the correction lens and the rear surface to the intersection point of the optical axis, is the distance from the focusing lens to the front surface of the correction lens, is the thickness of the correction lens, is the distance from the rear surface of the correction lens to the detector, is the distance from the intersection point of the light passing through the front surface of the correction lens and the optical axis to the center of the focusing lens, is the distance from the intersection point of the light passing through the front surface of the correction lens and the optical axis to the intersection point of the light passing through the rear surface of the correction lens and the optical axis, is the angle between the light and the optical axis.

7. The method for constructing a two-dimensional spectral map reduction model of a middle echelon grating spectrometer according to claim 3 or 5, characterized in that, If the said correction lens includes multiple lens groups, the offset of the light in the Y direction of the detector is specifically as follows: ； Among them, the correction lens includes multiple lens groups, and the offset of the light in the Y direction of the detector, is the distance between the light in the Y direction and the center of the focusing lens, , , , , , and are all the offsets of the light in the Y direction. The medium through which the light passes in the Y direction and the parameters of the correction lens are different, and the offsets are also different. and are both positive integers, and and are not equal to 1, 2, 3, 4, and 5. ≠ ; Then the offset of the light in the X direction of the detector is specifically as follows: ； Among them, the correction lens includes multiple lens groups, and the offset of the light in the X direction of the detector the distance between the light in the X direction and the center of the focusing lens , , , , , and are all the offsets of the light in the X direction. The medium through which the light passes in the X direction and the parameters of the correction lens are different, and the offsets are also different.

8. The method for constructing a two-dimensional spectrum reduction model of a echelle grating spectrometer according to claim 7, wherein Solve the described , , , , , , , , , , , , and , by the principle of geometric optics and considering the change in the refractive index of the medium through which the light passes.

9. The method for constructing a two-dimensional spectrum reduction model of a echelle grating spectrometer according to claim 1, wherein In the said Step S4, calibrating the two-dimensional spectrum reduction model for the echelle grating spectrometer based on a standard light source and optimizing the optical structure parameters in the two-dimensional spectrum reduction model includes the following steps: Step S401: Obtain the initial optical structure parameters in the constructed two-dimensional spectrum reduction model for the echelle grating spectrometer; The optical structure parameters in the constructed two-dimensional spectrum reduction model for the echelle grating spectrometer include the refractive index of the medium, the incident angle of the grating, the apex angle of the prism, the offset angle of the grating, and the system focal length; Step S402: Traverse the optical structure parameters in the constructed two-dimensional spectrum reduction model for the echelle grating spectrometer and generate the fitting coordinate positions of the two-dimensional spectrum reduction model for the echelle grating spectrometer; Step S403: Based on the characteristic wavelength of the standard light source, calculate the sum of the mean square errors between the fitting coordinate positions and the actual coordinate positions of the two-dimensional spectrum reduction model for the echelle grating spectrometer; Step S404: Judge whether the sum of the mean square errors reaches the minimum. If so, execute Step S405. If not, return to Step S402; Step S405: Complete the calibration and optimization of the optical structure parameters in the reconstructed two-dimensional spectral reduction model of the echelle grating spectrometer.

10. To construct a two-dimensional spectral map restoration model system for an echelle grating spectrometer, characterized in that, It includes the following modules: The first establishment module: Based on the principles of geometric optics and considering the change in the refractive index of the medium through which the light passes, establish the relationship between the wavelength in the Y direction of the echelle grating diffraction and the position of the detector pixel. The second establishment module: Based on the principles of geometric optics and considering the change in the refractive index of the medium through which the light passes, establish the relationship between the wavelength in the X direction of the prism dispersion and the position of the detector pixel. The construction module: Based on the established relationship between the wavelength in the Y direction of the echelle grating diffraction and the position of the detector pixel, and the established relationship between the wavelength in the X direction of the prism dispersion and the position of the detector pixel, construct a two-dimensional spectral reduction model of the echelle grating spectrometer. The calibration and optimization module: Calibrate the two-dimensional spectral reduction model of the echelle grating spectrometer based on a standard light source, optimize the optical structure parameters in the two-dimensional spectral reduction model, and obtain the optimal two-dimensional spectral reduction model of the echelle grating spectrometer.

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