Design method of free-form concave grating imaging spectrometer

Abstract

The application discloses a design method of a free curved surface concave grating imaging spectrometer, which comprises the following steps: S1, selecting a series of light rays incident from different positions of a slit as characteristic light rays; S2, calculating the coordinates and normal of a characteristic data point at the intersection of the characteristic light rays and a free curved surface concave grating surface; S3, obtaining an initial structure by fitting the free curved surface of the free curved surface concave grating; and S4, optimizing the initial structure. The application also relates to a free curved surface concave grating imaging spectrometer obtained by using the design method of the free curved surface concave grating imaging spectrometer.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of optical design, in particular to a design method of a free-form concave grating imaging spectrometer. BACKGROUND

[0002] Spectral information is very important and has a wide range of applications in the fields of biological science, medical health, pharmaceuticals, energy, food and agriculture. The acquisition of spectral information depends on spectrometers and imaging spectrometers. The key component in imaging spectrometers is an optical system with dispersion function. Optical systems with dispersion function have a larger field of view, a wider spectral range, and higher resolution, which can promote the development of related application fields and is the long-term goal pursued by people.

[0003] Free-form surface refers to a non-traditional surface that cannot be represented by spherical or aspherical coefficients. Free-form surface is a complex optical surface with no symmetry. In the past decade, the rapid development of free-form optics not only brings all-round improvement in the performance of optical systems, but also realizes many optical systems that were difficult to design or never existed before, bringing revolutionary breakthroughs in the field of optical design.

[0004] Existing imaging spectrometers rarely use free-form surfaces for design. The reason is that free-form surfaces have too many variables and too much freedom, and there are many factors to consider, such as system volume, weight, and number of lenses, making it difficult to design an imaging spectrometer with simple structure, low cost, and good imaging effect. SUMMARY

[0005] Therefore, it is necessary to provide a design method of a free-form concave grating imaging spectrometer, which can design a free-form concave grating imaging spectrometer with simple structure and good imaging effect.

[0006] A design method of a free-form concave grating imaging spectrometer, comprising the following steps:

[0007] S1, selecting a series of light rays incident from different positions of a slit as characteristic light rays;

[0008] S2, calculating the coordinates and normal of a characteristic data point at the intersection of the characteristic light rays and a free-form concave grating surface;

[0009] S3, obtaining the free-form surface shape of the free-form concave grating by fitting to obtain an initial structure; and

[0010] S4, optimizing the initial structure.

[0011] Compared with the prior art, the design method of the free-form concave grating imaging spectrometer provided by the application can obtain a free-form concave grating imaging spectrometer containing only one optical element, i.e., a free-form concave grating, which simultaneously serves as a dispersion element and an imaging element, so that the free-form concave grating imaging spectrometer has simple structure, small volume, low cost, and good imaging effect. BRIEF DESCRIPTION OF DRAWINGS

[0012] Figure 1 The optical path diagram of the free-form concave grating imaging spectrometer provided by the first embodiment of the application is shown.

[0013] Figure 2 The structural schematic diagram of the free-form concave grating imaging spectrometer provided by the first embodiment of the application is shown.

[0014] Figure 3 The wave aberration of the system 1 of the first embodiment of the application at different fields of view and different wavelengths is shown.

[0015] Figure 4 The flowchart of the design method of the free-form concave grating imaging spectrometer provided by the second embodiment of the application is shown.

[0016] MAIN ELEMENT SYMBOL EXPLANATION

[0017] Free-form concave grating imaging spectrometer 100

[0018] Slit 102

[0019] Concave grating 104

[0020] Detector 106

[0021] Image plane 108

[0022] The following specific embodiments will further illustrate the application in combination with the above drawings. DETAILED DESCRIPTION

[0023] The design method of the free-form concave grating imaging spectrometer provided by the application will be further described in detail below in combination with the drawings and specific embodiments.

[0024] Please refer to Figure 1 and Figure 2The first embodiment of the present application provides a free-form concave grating imaging spectrometer 100, which comprises a slit 102, a concave grating 104 and an image plane 108. Light is incident on the concave grating 104 through the slit 102, is dispersed and reflected to form a reflected light beam, and the reflected light beam is incident on the image plane 108 to form an image. The concave grating 104 has a free-form surface, so the concave grating 104 is a free-form concave grating 104. The free-form concave grating 104 simultaneously serves as a dispersion element and an imaging element of the free-form concave grating imaging spectrometer 100, that is, the free-form concave grating 104 simultaneously has the functions of dispersion and imaging. That is, light incident on the free-form concave grating 104 from the slit 102 is dispersed and reflected, and the reflected light beam is incident on the image plane 108, so that light of different wavelengths incident on the slit 102 is separated and imaged on the image plane 108, respectively.

[0025] The free-form concave grating imaging spectrometer 100 only contains a single optical element, which is the concave grating 104. That is, the free-form concave grating imaging spectrometer 100 only contains the concave grating 104 as an optical element. The slit 102 and the image plane 108 are located on the same side of the concave grating 104.

[0026] The slit 102 is a narrow and long slit hole with adjustable width. The slit 102 can be a fixed slit 102, a single-side adjustable asymmetric slit 102 and a double-side adjustable symmetric slit 102. In this embodiment, the slit 102 is a double-side adjustable symmetric slit 102.

[0027] The line distance of the concave grating 104 can be fixed or variable. When the line distance of the concave grating 104 is fixed, it means that the concave grating 104 has a fixed line distance, and the concave grating 104 is a fixed-line-distance concave grating 104. When the line distance of the concave grating 104 is variable, it means that the concave grating 104 has a variable line distance, and the concave grating 104 is a variable-line-distance concave grating 104. In one embodiment, the concave grating 104 is a fixed-line-distance free-form concave grating 104; in another embodiment, the concave grating 104 is a variable-line-distance free-form concave grating 104.

[0028] The line distance of the concave grating 104 can be fixed or variable. When the line distance of the concave grating 104 is fixed, it means that the concave grating 104 has a fixed line distance, and the concave grating 104 is a fixed-line-distance concave grating 104. When the line distance of the concave grating 104 is variable, it means that the concave grating 104 has a variable line distance, and the concave grating 104 is a variable-line-distance concave grating 104. In one embodiment, the concave grating 104 is a fixed-line-distance free-form concave grating 104; in another embodiment, the concave grating 104 is a variable-line-distance free-form concave grating 104.

[0029] d(x,y)=d0+d1y+d2y 2+d3y 3 +… (1)

[0030] The imaging optical system further comprises a detector 106, which is located at the position of the image plane 108, for recording the information of the image plane 108. The detector 106 can also be a film or the like. In the embodiment, the free curved concave grating imaging spectrometer 100 is composed of the slit 102, the concave grating 104, the image plane 108 and the detector 106.

[0031] Table 1 is the performance parameters of the free curved concave grating imaging spectrometer 100 when the concave grating 104 is different constant line spacing concave grating 104 and different variable line spacing concave grating 104. In Table 1, Constant indicates the constant line spacing concave grating 104, Variable indicates the variable line spacing concave grating 104, System No. indicates the system number (the system is the free curved concave grating imaging spectrometer 100, which is referred to as the system), Grating line-space indicates the line spacing of the concave grating 104, Spectral bandwidth indicates the spectral bandwidth, Spectral dispersion indicates the spectral dispersion, Slit length indicates the slit length, Numerical aperture indicates the numerical aperture, System length indicates the system length (the system length refers to the distance from the slit 102 to the concave grating 104), Spectral resolving power indicates the spectral resolving power, the unit of the spectral bandwidth is nm (nanometer), the unit of the spectral dispersion is nm / mm (nanometer per millimeter), and the units of the slit length and the system length are both mm (millimeter).

[0032] Table 1 is the performance parameters of the free curved concave grating imaging spectrometer 100

[0033]

[0034] As shown in Table 1, when the concave grating 104 is a fixed-pitch concave grating 104, the spectral range (spectral bandwidth) of the freeform concave grating imaging spectrometer 100 is 400 nm to 1000 nm, the spectral dispersion is greater than or equal to 240 nm / mm, the slit length 102 is less than or equal to 2.1 mm, the numerical aperture is less than or equal to 0.13, the system length is greater than or equal to 61 mm, and the spectral resolution can reach up to 342. When the concave grating 104 is a variable-pitch concave grating 104, the spectral range of the freeform concave grating imaging spectrometer 100 is 400 nm to 1000 nm, the spectral dispersion is greater than or equal to 100 nm / mm, the slit length 102 is less than or equal to 2.3 mm, the numerical aperture is less than or equal to 0.16, the system length is greater than or equal to 37 mm, and the spectral resolution can reach up to 820.

[0035] In Table 1, System No. 1 has a spectral range of 400 nm to 1000 nm, a slit length of 1 mm, a numerical aperture of 0.1, a system length of 100 mm, a maximum spectral dispersion of 340 nm / mm, and a spectral resolution of 241. At this point, the wavefront aberrations of System No. 1 at each field of view and wavelength are as follows: Figure 3 As shown.

[0036] Figure 3 In the figure, the horizontal axis represents the length of slit 102, and the vertical axis represents the wavelength. The length of slit 102 and the wavelength are both in mm. Figure 3 In the WFE RMS (wavefront error, root mean square), the minimum value is 0.0081λ, the maximum value is 0.0745λ, the average value is 0.0422λ, the standard deviation is 0.0065, the maximum keystone distortion is 0.175μm, and the maximum smile distortion is 0.109μm.

[0037] Depend on Figure 3 It can be seen that, within the entire working spectral range, the maximum RMS value of the full-field aberration of System 1 at each wavelength λ does not exceed 0.075λ. Therefore, the image quality (imaging quality) of System 1 at each wavelength reaches the diffraction limit, and System 1 has good image quality. The absolute values ​​of spectral line curvature and color distortion at each field point of System 1 at each wavelength do not exceed 1μm. The perpendicular distance from the image point on the image plane 108 of System 1 to the principal ray of the central field of view is not less than 1.4mm, avoiding obstruction. Furthermore, System 1 is object-side telecentric.

[0038] In addition, in Table 1, the maximum value of the wave aberration RMS of the full field of view in the spectral range of each of systems 2 to 21 is not more than 0.075λ, and the image quality reaches the diffraction limit, so that each of systems 2 to 21 has good image quality. The absolute value of the chromatic aberration and the spectral line curvature of each of systems 2 to 21 is less than 1 μm, so that each of systems 2 to 21 is free of obstruction, and each of systems 2 to 21 is object-side telecentric. Thus, the free-form concave grating imaging spectrometer 100 is object-side telecentric, free of obstruction, and has good image quality.

[0039] By comparing systems 1 to 21 using the constant-line-spacing concave grating 104 and the variable-line-spacing concave grating 104 in Table 1, the percentage of improvement in each performance parameter of the entire system using the variable-line-spacing concave grating 104 can be obtained, as shown in Table 2. In Table 2, Maximum improvement refers to the maximum improvement value, and From Constant To Variable refers to the change from the constant-line-spacing concave grating 104 to the variable-line-spacing concave grating 104.

[0040] Table 2 Percentage of improvement in each performance parameter of each system using the variable-line-spacing concave grating 104

[0041]

[0042] From Table 2, it can be seen that, when the spectral range is 400 nm to 1000 nm, using the variable-line-spacing concave grating 104, only the slit 102 length is increased by at most 80% from 1.0 mm to 1.8 mm; only the numerical aperture is increased by at most 40% from 0.10 to 0.14; only the system length is reduced by at most 92% from 100 mm to 52 mm; only the spectral dispersion is increased by at most 143% from 340 nm / mm to 140 nm / mm; and the spectral resolution can be as high as 585 in system 13, which is increased by 143% compared with system 1.

[0043] When the spectral range is 600 nm to 1000 nm, using the variable-line-spacing concave grating 104, only the slit 102 length is increased by at most 10% from 2.1 mm to 2.3 mm; only the numerical aperture is increased by at most 23% from 0.13 to 0.16; only the system length is reduced by at most 65% from 61 mm to 37 mm; only the spectral dispersion is increased by at most 140% from 240 nm / mm to 100 nm / mm; and the spectral resolution can be as high as 820 in system 17, which is increased by 140% compared with system 5.

[0044] When the spectral range is 400nm to 800nm, the variable-line- spacing concave grating 104 only improves the slit 102 length by up to 12% from 1.6mm to 1.8mm, the numerical aperture by up to 27% from 0.11 to 0.14, the system length by up to 40% from 73mm to 52mm, the spectral dispersion by up to 117% from 260nm / mm to 120nm / mm, and the spectral resolution by up to 117% to 683 in system 21, which is 117% higher than that in system 9.

[0045] From the above results, it can be seen that the variable-line-spacing concave grating 104 can improve the performance parameters of the system as a whole, and the effects of improving the spectral dispersion and spectral resolution and reducing the system length are particularly obvious. When the spectral range is 400nm to 1000nm, the improvement range of the performance parameters of the system is higher than that when the spectral range is 600nm to 1000nm and 400nm to 800nm, and the largest difference in the improvement range is the slit 102 length. The wavelength range of 400nm to 800nm has the relatively worst improvement effect due to the shorter average wavelength, which is consistent with the design rule of the imaging optical system.

[0046] Table 3 shows the decrease range of the best performance parameters of the system when the spectral range is reduced. In Table 3, the Decrease of best performance refers to the decrease of the best performance parameter.

[0047] Table 3 shows the decrease range of the best performance parameters of the system when the spectral range is reduced. In Table 3, the Decrease of best performance refers to the decrease of the best performance parameter.

[0048]

[0049] From Table 3, it can be seen that when the spectral range is expanded, the decrease range of the spectral dispersion and the spectral resolution of the system is large, and in the system using the fixed-line-spacing concave grating 104, the decrease range of the performance parameters is larger than that in the system using the variable-line-spacing concave grating 104. In addition, since the average wavelength in the spectral range of 400nm to 800nm is small, the system design is more difficult than that in the spectral range of 600nm to 1000nm. When the spectral range is expanded to 400nm to 1000nm, the system using the variable-line-spacing concave grating 104 does not improve in the slit 102 length, the numerical aperture, and the system length. Therefore, compared with the system using the fixed-line-spacing concave grating 104, the system using the variable-line-spacing concave grating 104 is not sensitive to the expansion of the spectral range, and thus the use of the variable-line-spacing concave grating 104 is beneficial to the expansion of the spectral range of the system.

[0050] The free-form concave grating imaging spectrometer 100 has the following advantages: first, using the high degree of freedom of the surface shape of the optical free-form surface, only one optical element is used to achieve high spectral imaging, that is, only the free-form concave grating 104 is contained, which simultaneously serves as a dispersion element and an imaging element, and the optical path is simple, the structure is simple, the volume is small, and the cost is low; second, the imaging effect is good; third, compared with using a fixed-line-spacing free-form concave grating 104, using a variable-line-spacing free-form concave grating 104 can improve the performance of the free-form concave grating imaging spectrometer 100, and is particularly effective in improving spectral dispersion and spectral resolution, reducing system length, and is also beneficial to expanding the spectral range. The second embodiment of the present application provides a design method of the free-form concave grating imaging spectrometer 100, which is: first, determining the initial structure of the free-form concave grating imaging spectrometer 100, and then optimizing the initial structure. In the design method, a point-by-point design method for an optical system with a dispersion device is used to solve the initial structure, the point-by-point design method is: first, selecting a series of light rays incident from different positions of the slit 102 as characteristic light rays, then calculating the coordinates and normals of the characteristic data points at the intersection points of the characteristic light rays and the concave grating 104 surface, then obtaining the free-form surface shape of the concave grating 104 by fitting, and obtaining the initial structure. Finally, the imaging quality of the initial structure is improved by optimization to obtain the free-form concave grating imaging spectrometer 100.

[0051] Please refer to Figure 4 The design method of the free-form concave grating imaging spectrometer 100 includes the following steps:

[0052] S1, selecting a series of light rays incident from different positions of the slit 102 as characteristic light rays;

[0053] S2, calculating the coordinates and normals of the characteristic data points at the intersection points of the characteristic light rays and the concave grating 104 surface;

[0054] S3, obtaining the free-form surface shape of the concave grating 104 by fitting to obtain an initial structure; and

[0055] S4, optimizing the initial structure.

[0056] In step S2, the concave grating 104 is a free-form concave grating 104. When the surface shape of the concave grating 104 is calculated using the point-by-point design method, first, the coordinates of each feature data point on the surface of the concave grating 104 are calculated according to the principle of the nearest ray. Then, the normal of each feature data point on the surface of the concave grating 104 is calculated according to the object-image relationship of the system. According to the imaging requirements of the system, the light rays emitted from different positions on the slit 102 are finally to be converged at the target point (i.e., the ideal image point) on the image plane 108. Therefore, for a certain feature light ray, when the wavelength is λ, the direction vector S of the incident light ray at the corresponding feature data point on the surface of the concave grating 104 and the direction vector S' of the outgoing light ray should satisfy the grating equation. According to the generalized tracing equation of the grating given by Ludwig, S and S' should satisfy

[0057]

[0058] wherein n represents the diffraction order, λ represents the wavelength of the light ray, G represents the normal direction of the grating generating surface, R represents the normal of the feature data point, and d represents the grating line distance at the point of incidence of the light ray. Among them, n, λ and G are known quantities, and R and d are unknown quantities.

[0059] The calculation method of the normal of each feature data point on the surface of the concave grating 104 is different according to the type of the concave grating 104. That is, the calculation method of the normal of each feature data point on the surface of the constant-line-spacing concave grating 104 is different from the calculation method of the normal of each feature data point on the surface of the variable-line-spacing concave grating 104. The following is a specific description.

[0060] When the surface shape of the constant-line-spacing concave grating 104 is calculated, the grating line distance d0 is first calculated. According to the size of the spectral dispersion of the system and the distance from the surface of the concave grating 104 to the image plane 108, the size of the dispersion angle of the chief ray at the center of the slit 102 can be calculated, and according to the size of the dispersion angle and the spectral range, the grating line distance d0 that meets the requirements can be calculated. At this time, all the known quantities in formula (2) are known except R, so the value of R can be solved to obtain the normal of each feature data point on the surface of the constant-line-spacing concave grating 104. That is, the method for calculating the normal of each feature data point on the surface of the constant-line-spacing concave grating 104 comprises the following sub-steps:

[0061] S21', according to the size of the spectral dispersion of the system and the distance from the surface of the constant-line-spacing concave grating to the image plane, the size of the dispersion angle of the chief ray at the center of the slit is calculated;

[0062] S22', according to the size of the dispersion angle and the spectral range, the grating line distance d0 that meets the requirements is calculated;

[0063] S23', according to formula Solving the value of R, wherein n represents the diffraction order, λ represents the wavelength of the light, G represents the normal direction of the grating generating surface, R represents the normal of each feature data point on the ruled surface grating surface, d represents the grating line distance at the light incident point, S represents the direction vector of the incident light at the corresponding feature data point on the ruled surface grating 104 surface, and S' represents the direction vector of the outgoing light at the corresponding feature data point on the ruled surface grating 104 surface.

[0064] When the surface shape of the variable-line-space concave grating 104 is calculated, the grating line distance at different feature data points is different, and the following method is adopted for solving:

[0065] S21, the surface shape of the grating is set to a spherical surface, the intersection of the characteristic light and the spherical surface is the feature data point, the normal of the spherical surface at each feature data point is known, at this time, all known quantities in formula (2) except d can be solved, so the grating line distance d at this feature data point can be solved, when the grating line distance at all feature data points is solved, the function d(y) of the grating line distance with the coordinate y is fitted according to formula (1); and

[0066] S22, the normal R of the feature data point of the ruled surface grating 104 is solved by the method of solving the normal of the feature data point of the ruled surface grating 104 (i.e. the step S23'), but the difference is that the value of the grating line distance d at each feature data point is not solved according to the dispersion of the center chief ray of the slit 102, but is given by the function d(y).

[0067] In step S3, after the coordinates and normals of all feature data points are solved, the free surface surface shape of the ruled surface grating 104 or the free surface surface shape of the variable-line-space concave grating 104 is obtained by fitting.

[0068] The method of fitting the free surface surface shape of the concave grating 104 is not limited. In the embodiment, the method of fitting the free surface surface shape of the concave grating 104 includes the following sub-steps:

[0069] Step S1', an initial surface and a first three-dimensional rectangular coordinate system are established;

[0070] Step S2', K characteristic light rays R i (i=1, 2, …, K) are selected;

[0071] Step S3', the multiple intersection points of each characteristic light and the to-be-solved free surface are solved point by point according to the object-image relationship or the light ray mapping relationship and Snell's law, and then multiple feature data points P i (i=1, 2, …, K) are obtained;

[0072] Step S4', fitting the plurality of feature data points into a spherical surface in the first three-dimensional rectangular coordinate system, defining the feature data point corresponding to the center sampling view main light as the vertex of the spherical surface, and establishing a second three-dimensional rectangular coordinate system with the vertex of the spherical surface as the origin and the straight line between the center of curvature and the vertex of the spherical surface as the z-axis; and

[0073] Step S5', transforming the coordinates (x i ,y i ,z i ) and normal vectors (α i ,β i ,γ i ) of the plurality of feature data points in the first three-dimensional rectangular coordinate system into coordinates (x' i ,y' i ,z' i ) and normal vectors (α' i ,β' i ,γ' i ) in the second three-dimensional rectangular coordinate system, fitting the plurality of feature data points P i (i=1,2…K) in the second three-dimensional rectangular coordinate system into a quadric surface, removing the coordinates and normal vectors of the feature data points on the quadric surface in the second three-dimensional rectangular coordinate system from the coordinates (x' i ,y' i ,z' i ) and normal vectors (α' i ,β' i ,γ' i ) to obtain residual coordinates and residual normal vectors, and performing surface fitting on the residual coordinates and residual normal vectors to obtain a free surface, and adding the equation of the free surface to the equation of the quadric surface to obtain the equation of the free surface of the concave grating 104.

[0074] In step S4, the purpose of optimizing the initial structure is to improve the imaging quality of the initial structure. The method of optimizing the initial system to improve the imaging quality of the initial system is not limited, and can be realized by using optical design software. The optical design software includes CODE V or ZEMAX OPTIC STUDIO, etc.

[0075] Further, the design method of the free-form concave grating imaging spectrometer 100 can further include a step of processing according to the parameters output in step S4 after step S4, so as to obtain a physical element of the free-form concave grating imaging spectrometer 100, which has a shape, is made of a material, and is a physical element entity.

[0076] In addition, for the variable-line-spacing concave grating 104, a function of the grating spacing changing with coordinates is obtained while the free-form surface profile is solved. In order to further improve the solving effect of the variable-line-spacing concave grating 104 and the initial system image quality, the step S3 of the design method of the free-form concave grating imaging spectrometer 100 further comprises the following steps:

[0077] S31, fixing the solved free-form surface profile, repeating the step S21 in the variable-line-spacing concave grating 104 surface profile solving process, and calculating a new grating spacing change function;

[0078] S32, repeating the step S22 in the variable-line-spacing concave grating 104 surface profile solving process, and obtaining a corresponding new free-form surface profile; and

[0079] S33, iteratively repeating the step S31 and the step S32, and the imaging quality of the calculated variable-line-spacing free-form concave grating imaging spectrometer 100 can be further improved.

[0080] In the embodiment, the design method of the free-form concave grating imaging spectrometer 100 is used to obtain the system 1 to the system 21.

[0081] The design method of the free-form concave grating imaging spectrometer 100 has the following advantages: first, an initial solution meeting the given conditions can be quickly generated, and a high-image-quality system can be obtained through subsequent optimization, which greatly facilitates the design of systems with different spectral ranges and different spectral resolutions; second, the method is simple.

[0082] In addition, those skilled in the art can make other changes within the spirit of the present application, and of course, these changes made according to the spirit of the present application should be included in the scope of protection claimed by the present application.

Claims

1. A design method for a freeform concave grating imaging spectrometer, characterized in that, The spectrometer comprises a free-form concave grating having a free-form surface, the free-form concave grating simultaneously serving as a dispersion element and an imaging element, and the method comprises the following steps: S1, selecting a series of light rays incident from different positions of a slit as characteristic light rays; S21, calculating the coordinates of the feature data points at the intersection of the feature light rays and the free-form surface; setting the surface shape of the variable-pitch free-form surface concave grating as a spherical surface, the intersection of the feature light rays and the spherical surface being the feature data points, the spherical surface normal R at each feature data point being known, at this time the formula is used to solve the grating pitch d at the feature data point, where all the quantities except d are known, thereby solving the grating pitch d at the feature data point, when the grating pitches at all the feature data points are solved, the function d(y) of the grating pitch varying with the coordinates y is fitted according to the formula ​ S22, according to the formula Solve the value of R, wherein n represents the diffraction order, λ represents the wavelength of the light, G represents the normal direction of the grating generating surface, R represents the normal of each feature data point on the variable-line-spacing free-form concave grating surface, d represents the grating line spacing at the light incidence point, S represents the direction vector of the incident light at the corresponding feature data point on the variable-line-spacing free-form concave grating surface, and S' represents the direction vector of the outgoing light at the corresponding feature data point on the variable-line-spacing free-form concave grating surface. S3, obtaining an initial structure by fitting the free-form surface of the free-form concave grating, wherein the grating line spacing at different characteristic data points of the free-form surface is different; and S4, optimizing the initial structure.

2. The method of designing a freeform concave grating imaging spectrometer according to claim 1, wherein, The step S3 further comprises the following steps: S31, fixing the obtained free-form surface shape, repeating the step S21, and calculating a new grating line spacing change function; S32, repeating the step S22 again to obtain a corresponding new free-form surface shape; and S33, repeatedly repeating the steps S31 and S32 for iteration.

3. The method of designing a freeform concave grating imaging spectrometer according to claim 1, wherein, In the step S4, an optical design software is used to optimize the initial structure.

4. The method of designing a freeform concave grating imaging spectrometer according to claim 1, wherein, The design method of the free-form concave grating imaging spectrometer further comprises a step of processing according to the parameters output in the step S4 after the step S4, so as to obtain a physical element of the free-form concave grating imaging spectrometer.

5. The method of designing a freeform concave grating imaging spectrometer according to claim 1, wherein, The free-form concave grating imaging spectrometer comprises a slit, a free-form concave grating and an image plane, light rays from an object are irradiated onto the free-form concave grating through the slit and form a reflected light beam by reflection, and the reflected light beam is irradiated onto the image plane to form an image.

6. The method of designing a freeform concave grating imaging spectrometer according to claim 5, wherein, The free-form concave grating imaging spectrometer only contains one optical element of the free-form concave grating.

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