Spectroscopic imaging method and system for snapshot imaging spectrometer

Abstract

The present application relates to a kind of snapshot imaging spectrometer's spectroscopic imaging method and its system.Spectroscopic imaging system is off-axis three reverse structure, and working wave band is 400nm~800nm;According to the direction of light incidence, it includes the first free curved surface mirror that is curved to the direction of light incidence in approximate concentric structure, the convex surface diffraction grating that is curved to the direction of light incidence in the direction of light incidence in reverse and the second free curved surface mirror that is curved to the direction of light incidence, filter and two respectively for focusing the monochromatic light of different wavelength that is reflected or transmitted by filter photoelectric sensor.The spectroscopic imaging method used in the present application can realize the full visible light wave band coverage of working wave band, effectively balances various monochromatic aberrations, and achieves the imaging effect close to diffraction limit;Spectroscopic imaging system has the characteristics of large relative aperture, high spectral resolution, wide working wave band, no chromatic aberration, light and small volume.

Description

Technical Field

[0001] This invention relates to spectroscopic imaging technology for imaging spectrometers, specifically to a reflective spectroscopic imaging system and imaging method for a snapshot imaging spectrometer. Background Technology

[0002] Spectral imaging technology is a multi-dimensional information acquisition technique that integrates optical imaging and spectral analysis. It can simultaneously acquire both two-dimensional spatial information and one-dimensional spectral information of the target object. Based on this, researchers can measure and analyze the chemical structure, state information, and content of the substances composing the target object according to its spectral characteristics. Therefore, this technology has broad application prospects in fields such as production, daily life, scientific research, and military reconnaissance.

[0003] Traditional spectral imaging techniques mostly use slits to segment the field of view and obtain a linear field of view spectral image. By pushing the target to form an image, a full field of view spectral image can be obtained. These systems have low energy efficiency and long scanning time, and cannot meet the needs of dynamic target spectral imaging.

[0004] Snapshot spectral imaging technology can acquire two-dimensional spatial information and one-dimensional spectral information of a target object within a detector integration time without pushbroom, meeting the needs of some applications that require real-time acquisition of spatial and spectral information. The spectroscopic imaging system is the core component of a snapshot imaging spectrometer, and its imaging quality determines the spectral resolution and imaging performance of the snapshot imaging spectrometer.

[0005] Existing spectroscopic imaging systems commonly used in snapshot imaging spectrometers are mainly transmission-type or folding-back systems. These two types of imaging systems suffer from low light energy utilization, large chromatic aberration, and narrow operating wavelengths. The literature "Optical Design of a Novel Snapshot Spectroscopic Imaging System Based on Dyson Structure" (DOI: 10.3788 / aos202242.0422002) discloses a folding-back spectroscopic imaging system for snapshot imaging spectrometers. The system operates in the 450nm–650nm wavelength range with a numerical aperture (NA) of 0.3. The system employs a concentric Dyson structure, which effectively balances various monochromatic aberrations and achieves large numerical aperture imaging. However, this system suffers from chromatic aberration introduced by the transmission optical elements, resulting in an operating wavelength bandwidth of only 200nm.

[0006] Therefore, this paper proposes a spectroscopic imaging method and system suitable for snapshot imaging spectrometers to address the shortcomings of current snapshot spectroscopic imaging systems, which have narrow operating bands. This has practical significance for the promotion and application of snapshot spectroscopic imaging technology. Summary of the Invention

[0007] This invention addresses the shortcomings of existing technologies by providing a spectroscopic imaging system and imaging method for a snapshot imaging spectrometer that features a wide operating band, high imaging quality, small size, and compact structure.

[0008] The technical solution to achieve the purpose of this invention is to provide a spectroscopic imaging system for a snapshot imaging spectrometer. The spectroscopic imaging system is an off-axis three-reflection structure. It includes, in sequence according to the light incident direction, a first freeform surface mirror bent towards the light incident direction, a quadratic convex diffraction grating bent away from the light incident direction, a second freeform surface mirror bent towards the light incident direction, a filter, and two photoelectric sensors for focusing monochromatic light of different wavelengths reflected or transmitted by the filter. The first freeform surface mirror, the quadratic convex diffraction grating, and the second freeform surface mirror are approximately concentric. The system aperture is located on the quadratic convex diffraction grating.

[0009] The reflecting surface of the first freeform mirror is an XY polynomial freeform surface. In a Cartesian coordinate system with the vertex of the first freeform mirror as the origin O, the incident direction of light as the positive Z-axis, the positive Y-axis upward, and the positive X-axis inward, the expression Z1 of the reflecting surface of the first freeform mirror is:

[0010] ;

[0011] In the formula, c is the curvature, c=0.0259, k is the quadratic surface coefficient, k=0.005218, C2~C 20 These are the coefficients of each monomial, with a range of -4 × 10⁻⁶. -3 ≤C2≤-3×10 -3 -3×10 -6 ≤C3≤-2×10 -6 -3×10 -5 ≤C4≤-2×10 -5 -2×10 -7 ≤C5≤-1×10 -7 -2×10 -6 ≤C6≤-1×10 -6 -2×10 -8 ≤C7≤-1×10 -8 -9×10 -8 ≤C8≤-8×10 -8 4×10 -8 ≤C9≤5×10 -8 1×10 -10 ≤C 10 ≤2×10 -10 2×10 -9 ≤C 11 ≤3×10 -9-4×10 -9 ≤C 12 ≤-3×10 -9 -4×10 -12 ≤C 13 ≤-3×10 -12 -3×10 -11 ≤C 14 ≤-2×10 -11 -6×10 -11 ≤C 15 ≤-5×10 -11 -10×10 -11 ≤C 16 ≤-9×10 -11 -2×10 -13 ≤C 17 ≤-1×10 -13 -6×10 -13 ≤C 18 ≤-5×10 -13 -7×10 -13 ≤C 19 ≤-6×10 -13 -2×10 -12 ≤C 20 ≤-1×10 -12 ;

[0012] The surface shape Z2 expression of the quadric convex diffraction grating is:

[0013] ;

[0014] In the formula, r is the aperture radius of the quadric convex diffraction grating; k0 is the quadric coefficient, 0.35≤k0≤0.4; c0 is the curvature, -0.05≤c0≤-0.04; and the grating line density is g, 250 lines / mm≤g≤270 lines / mm.

[0015] The reflecting surface of the second freeform mirror is an XY polynomial freeform surface. In a Cartesian coordinate system with the vertex of the second freeform mirror as the origin O, the incident direction of light as the positive Z-axis, the positive Y-axis upward, and the positive X-axis inward, the expression Z3 of the reflecting surface of the second freeform mirror is:

[0016] ;

[0017] In the formula, x and y are the coordinates of any point on the mirror surface, b is the curvature, b = -0.0229, k1 is the quadratic surface coefficient, k1 = 0.92, and B2 to B... 20 These are the coefficients of each monomial, with a range of -7 × 10⁻⁶. -3 ≤B2≤-6×10-3 -3×10 -5 ≤B3≤-2×10 -5 -3×10 -5 ≤B4≤-2×10 -5 -2×10 -6 ≤B5≤-1×10 -6 -4×10 -6 ≤B6≤-3×10 -6 1×10 -7 ≤B7≤2×10 -7 1×10 -7 ≤B8≤2×10 -7 -2×10 -8 ≤B9≤-1×10 -8 -3×10 -9 ≤B 10 ≤-2×10 -9 -2×10 -8 ≤B 11 ≤-1×10 -8 -2×10 -8 ≤B 12 ≤-1×10 -8 2×10 -11 ≤B 13 ≤3×10 -11 -2×10 -10 ≤B 14 ≤-1×10 -10 -4×10 -10 ≤B 15 ≤-3×10 -10 -3×10 -10 ≤B 16 ≤-2×10 -10 -2×10 -12 ≤B 17 ≤-1×10 -12 -8×10 -12 ≤B 18 ≤-7×10 -12 -9×10 -12 ≤B 19 ≤-8×10 -12 -4×10 -12 ≤B 20 ≤=-3×10 -12 ;

[0018] The filter operates in the wavelength range of 400nm to 800nm, of which 400nm to 600nm is the reflection band and 600nm to 800nm ​​is the transmission band.

[0019] The present invention provides a spectroscopic imaging system for a snapshot imaging spectrometer, wherein the working F-number ranges from 2.8 to 3.2.

[0020] The technical solution of the present invention also includes a spectroscopic imaging method for a snapshot imaging spectrometer, the steps of which are as follows:

[0021] (1) Polychromatic incident light with wavelengths of 400nm to 800nm ​​is reflected by the first free-form surface mirror bent in the direction of light incidence and then incident on the convex diffraction grating of the quadratic surface bent in the direction of light incidence.

[0022] The reflecting surface of the first freeform mirror is an XY polynomial freeform surface. In a Cartesian coordinate system with the vertex of the first freeform mirror as the origin O, the incident direction of light as the positive Z-axis, the positive Y-axis upward, and the positive X-axis inward, the expression Z1 of the reflecting surface of the first freeform mirror is:

[0023] ;

[0024] In the formula, c is the curvature, c=0.0259, k is the quadratic surface coefficient, k=0.005218, C2~C 20 These are the coefficients of each monomial, with a range of -4 × 10⁻⁶. -3 ≤C2≤-3×10 -3 -3×10 -6 ≤C3≤-2×10 -6 -3×10 -5 ≤C4≤-2×10 -5 -2×10 -7 ≤C5≤-1×10 -7 -2×10 -6 ≤C6≤-1×10 -6 -2×10 -8 ≤C7≤-1×10 -8 -9×10 -8 ≤C8≤-8×10 -8 4×10 -8 ≤C9≤5×10 -8 1×10 -10 ≤C 10 ≤2×10 -10 2×10 -9 ≤C 11 ≤3×10 -9 -4×10 -9 ≤C 12 ≤-3×10 -9 -4×10 -12 ≤C 13 ≤-3×10-12 -3×10 -11 ≤C 14 ≤-2×10 -11 -6×10 -11 ≤C 15 ≤-5×10 -11 -10×10 -11 ≤C 16 ≤-9×10 -11 -2×10 -13 ≤C 17 ≤-1×10 -13 -6×10 -13 ≤C 18 ≤=-5×10 -13 -7×10 -13 ≤C 19 ≤-6×10 -13 -2×10 -12 ≤C 20 ≤=-1×10 -12 ;

[0025] The surface shape Z2 expression of the quadric convex diffraction grating is:

[0026] ;

[0027] In the formula, r is the aperture radius of the quadric convex diffraction grating; k0 is the quadric coefficient, 0.35≤k0≤0.4; c0 is the curvature, -0.05≤c0≤-0.04; and the grating line density is g, 250 lines / mm≤g≤270 lines / mm.

[0028] (2) After being split by the quadric convex diffraction grating, each monochromatic light is reflected at different diffraction angles and incident on the second free-form surface mirror that bends toward the direction of light incidence.

[0029] The reflecting surface of the second freeform mirror is an XY polynomial freeform surface. In a Cartesian coordinate system with the vertex of the second freeform mirror as the origin O, the incident direction of light as the positive Z-axis, the positive Y-axis upward, and the positive X-axis inward, the expression Z3 of the reflecting surface of the second freeform mirror is:

[0030] ;

[0031] In the formula, x and y are the coordinates of any point on the mirror surface, b is the curvature, b = -0.0229, k1 is the quadratic surface coefficient, k1 = 0.92, and B2 to B... 20 These are the coefficients of each monomial, with a range of -7 × 10⁻⁶. -3 ≤B2≤-6×10 -3 -3×10-5 ≤B3≤-2×10 -5 -3×10 -5 ≤B4≤-2×10 -5 -2×10 -6 ≤B5≤-1×10 -6 -4×10 -6 ≤B6≤-3×10 -6 1×10 -7 ≤B7≤2×10 -7 1×10 -7 ≤B8≤2×10 -7 -2×10 -8 ≤B9≤-1×10 -8 -3×10 -9 ≤B 10 ≤-2×10 -9 -2×10 -8 ≤B 11 ≤-1×10 -8 -2×10 -8 ≤B 12 ≤-1×10 -8 2×10 -11 ≤B 13 ≤3×10 -11 -2×10 -10 ≤B 14 ≤-1×10 -10 -4×10 -10 ≤B 15 ≤-3×10 -10 -3×10 -10 ≤B 16 ≤-2×10 -10 -2×10 -12 ≤B 17 ≤-1×10 -12 -8×10 -12 ≤B 18 ≤-7×10 -12 -9×10 -12 ≤B 19 ≤-8×10 -12 -4×10 -12 ≤B 20 ≤-3×10 -12 ;

[0032] (3) A filter is used to filter several beams of monochromatic light of different wavelengths reflected by the second freeform surface mirror. The light with wavelengths of 400nm to 600nm is reflected by the filter and focused on the photoelectric sensor. The light with wavelengths of 600nm to 800nm ​​is transmitted through the filter and focused on another photoelectric sensor.

[0033] Compared with the prior art, the beneficial effects of the present invention are:

[0034] 1. This invention employs an off-axis three-mirror beam splitting imaging method and beam splitting imaging system structure, eliminating the introduction of chromatic aberration and achieving full visible light band coverage from 400nm to 800nm. At the same time, the beam splitting imaging system also features small size and compact structure.

[0035] 2. The spectroscopic imaging system provided by the present invention has two free-form surfaces for its two reflecting mirrors and a quadratic surface for its convex diffraction grating. Therefore, it can better balance various monochromatic aberrations and achieve an imaging effect close to the diffraction limit. Attached Figure Description

[0036] Figure 1 This is a schematic diagram of the structure of the spectroscopic imaging system provided in an embodiment of the present invention;

[0037] In the figure, 1. First freeform surface mirror; 2. Quadratic convex surface diffraction grating; 3. Second freeform surface mirror; 4. Filter; 5. First photoelectric sensor; 6. Second photoelectric sensor.

[0038] Figure 2 This is a schematic diagram illustrating the beam splitting imaging principle of the beam splitting imaging system within the meridional plane provided in this embodiment of the invention;

[0039] Figure 3 This is a simplified optical path diagram of different diffraction orders of the spectroscopic imaging system provided in the embodiments of the present invention;

[0040] Figure 4 This is a distortion curve diagram of the spectroscopic imaging system provided in the embodiments of the present invention;

[0041] Figure 5 This is a ray tracing point array diagram of the image plane of the spectroscopic imaging system provided in this embodiment of the invention;

[0042] Figure 6 This is a graph of the MTF (Mean Transfer Function) curve of the spectroscopic imaging system provided in this embodiment of the invention. Detailed Implementation

[0043] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0044] Example 1:

[0045] The technical solution of this embodiment is to provide a spectroscopic imaging system and imaging method for a snapshot imaging spectrometer.

[0046] The spectroscopic imaging system provided in this embodiment has a magnification of -1, an object-side numerical aperture NA of 0.17, an object-side field of view Φ of 4mm × 1mm, and a working wavelength of 400nm to 800nm.

[0047] See appendix Figure 1 This is a schematic diagram of the spectroscopic imaging system provided in this embodiment. The spectroscopic imaging system is an off-axis three-mirror structure. According to the direction of light incidence, it includes a first freeform surface mirror 1; a quadrature convex surface diffraction grating 2; a second freeform surface mirror 3; a filter 4; and two first photoelectric sensors 5 or second photoelectric sensors 6, respectively used to focus several beams of monochromatic light of different wavelengths reflected or transmitted by the filter. The first freeform surface mirror is bent towards the direction of light incidence, the quadrature convex surface diffraction grating is away from the direction of light incidence, and the second freeform surface mirror is bent towards the direction of light incidence. The first freeform surface mirror, the quadrature convex surface diffraction grating, and the second freeform surface mirror are approximately concentric. The system aperture is located on the quadrature convex surface diffraction grating.

[0048] See appendix Figure 2 This is a schematic diagram of the beam splitting imaging principle of the beam splitting imaging system in the meridional plane provided in this embodiment. Compared with the existing slit-type pushbroom beam splitting imaging system, which requires multiple scans to obtain a spectral image with a certain meridional field of view, the beam splitting imaging system provided in this embodiment can obtain a spectral image with a certain meridional field of view in a single imaging.

[0049] According to the appendix Figure 2 The optical path shown illustrates the principle of spectral imaging. The steps of the spectral imaging method for the snapshot imaging spectrometer provided in this embodiment are as follows:

[0050] (1) Polychromatic incident light with wavelengths of 400nm to 800nm ​​is reflected by the first free-form surface mirror 1, which is bent in the direction of light incident, and then incident on the quadratic convex surface diffraction grating 2, which is bent in the opposite direction of light incident.

[0051] The reflecting surface of the first freeform mirror is an XY polynomial freeform surface. In a Cartesian coordinate system with the vertex of the first freeform mirror as the origin O, the incident direction of light rays as the positive Z-axis, the positive Y-axis upward, and the positive X-axis inward, the expression Z1 of the reflecting surface of the first freeform mirror is:

[0052] ;

[0053] In the formula, c is the curvature, c=0.0259, k is the quadratic surface coefficient, k=0.005218, C2~C 20 These are the coefficients of each monomial, with a range of -4 × 10⁻⁶. -3 ≤C2≤-3×10 -3-3×10 -6 ≤C3≤-2×10 -6 -3×10 -5 ≤C4≤-2×10 -5 -2×10 -7 ≤C5≤-1×10 -7 -2×10 -6 ≤C6≤-1×10 -6 -2×10 -8 ≤C7≤-1×10 -8 -9×10 -8 ≤C8≤-8×10 -8 4×10 -8 ≤C9≤5×10 -8 1×10 -10 ≤C 10 ≤2×10 -10 2×10 -9 ≤C 11 ≤3×10 -9 -4×10 -9 ≤C 12 ≤-3×10 -9 -4×10 -12 ≤C 13 ≤-3×10 -12 -3×10 -11 ≤C 14 ≤-2×10 -11 -6×10 -11 ≤C 15 ≤-5×10 -11 -10×10 -11 ≤C 16 ≤-9×10 -11 -2×10 -13 ≤C 17 ≤-1×10 -13 -6×10 -13 ≤C 18 ≤-5×10 -13 -7×10 -13 ≤C 19 ≤-6×10 -13 -2×10 -12 ≤C 20 ≤-1×10 -12 ;

[0054] The surface shape Z2 expression of a quadric convex diffraction grating is:

[0055] ;

[0056] In the formula, r is the aperture radius of the quadric convex diffraction grating; k0 is the quadric coefficient, 0.35≤k0≤0.4; c0 is the curvature, -0.05≤c0≤-0.04; and the grating line density is g, 250 lines / mm≤g≤270 lines / mm.

[0057] (2) After being split by the quadratic convex diffraction grating, each monochromatic light is incident on the second free-form surface mirror 3, which is bent in the direction of light incidence;

[0058] The reflecting surface of the second freeform mirror is an XY polynomial freeform surface. In a Cartesian coordinate system with the vertex of the second freeform mirror as the origin O, the incident direction of light rays as the positive Z-axis, the positive Y-axis upward, and the positive X-axis inward, the expression Z3 for the reflecting surface of the second freeform mirror is:

[0059] ;

[0060] In the formula, x and y are the coordinates of any point on the mirror surface, b is the curvature, b = -0.0229, k1 is the quadratic surface coefficient, k1 = 0.92, and B2 to B... 20 These are the coefficients of each monomial, with a range of -7 × 10⁻⁶. -3 ≤B2≤-6×10 -3 -3×10 -5 ≤B3≤-2×10 -5 -3×10 -5 ≤B4≤-2×10 -5 -2×10 -6 ≤B5≤-1×10 -6 -4×10 -6 ≤B6≤-3×10 -6 1×10 -7 ≤B7≤2×10 -7 1×10 -7 ≤B8≤2×10 -7 -2×10 -8 ≤B9≤-1×10 -8 -3×10 -9 ≤B 10 ≤-2×10 -9 -2×10 -8 ≤B 11 ≤-1×10 -8 -2×10 -8 ≤B 12 ≤-1×10 -8 2×10 -11 ≤B 13 ≤3×10 -11 -2×10 -10 ≤B14 ≤-1×10 -10 -4×10 -10 ≤B 15 ≤-3×10 -10 -3×10 -10 ≤B 16 ≤-2×10 -10 -2×10 -12 ≤B 17 ≤-1×10 -12 -8×10 -12 ≤B 18 ≤-7×10 -12 -9×10 -12 ≤B 19 ≤-8×10 -12 -4×10 -12 ≤B 20 ≤-3×10 -12 ;

[0061] (3) A filter 4 is used to filter several beams of monochromatic light of different wavelengths reflected by the second freeform surface mirror. The light with wavelengths of 400nm to 600nm is reflected by the filter and focused on the photoelectric sensor 5. The light with wavelengths of 600nm to 800nm ​​is transmitted through the filter and focused on another photoelectric sensor 6.

[0062] See appendix Figure 3 This is a simplified schematic diagram of the optical paths of different diffraction orders in the spectroscopic imaging system provided in this embodiment; the first freeform surface mirror 1 and the quadratic convex surface diffraction grating 2 are simplified as mirrors. Unlike traditional slit-type pushbroom spectroscopic imaging systems, the imaging field of view in this embodiment is a planar field of view; therefore, spectral stacking is a key focus of research for this type of system. In the object-side field of view, the distances y1 and y2 from point C at the lower boundary can be expressed as:

[0063]

[0064]

[0065] Where h is the off-axis measurement of the field of view, and Δh is the half-width of the field of view in the dispersion direction. The distance from the upper limit of the first-order spectrum to point C is expressed as:

[0066]

[0067] Where λ2 is the long-wavelength boundary wavelength, g is the grating line density, and r is the radius of curvature of the quadratic convex diffraction grating.

[0068] The distance from the lower limit of the secondary spectrum to point C is expressed as:

[0069]

[0070] Where λ1 is the shortwave boundary wavelength.

[0071] The upper limit of the first-order spectrum and the lower limit of the second-order spectrum are the first to cause an overlap problem. To avoid overlap, then:

[0072]

[0073] That is, the field width 2Δh in the dispersion direction must satisfy:

[0074]

[0075] In this embodiment, the incident wavelength range is 400nm to 800nm. When λ1 = 400nm and λ2 = 800nm, the calculated field width must be less than or equal to 0. That is, without using a filter, the superposition problem between the first-order and second-order spectra cannot be avoided. Therefore, a filter is used to divide the working wavelength range into 400nm to 600nm and 600nm to 800nm ​​to obtain a certain field of view in the dispersion direction.

[0076] The structural parameters of each component of the optical system provided in this embodiment are shown in Table 1.

[0077] Table 1

[0078] .

[0079] See appendix Figure 4 This is a distortion curve diagram of the spectroscopic imaging system provided in this embodiment. The horizontal axis represents the distortion value (in %) relative to the image plane, and the vertical axis represents the normalized field of view. Figure 4 The results show that the distortion aberrations of the spectroscopic imaging system have been adequately corrected, with a relative distortion of less than 0.2%.

[0080] See appendix Figure 5 It is a ray tracing point map of light passing through the spectral imaging system provided in this embodiment. The root mean square radius of the point map corresponding to each field of view at different wavelengths in the figure is less than 2μm, the geometric radius of the point map is less than 3μm, and the imaging quality is good.

[0081] See appendix Figure 6 This refers to the MTF (Mean Transfer Function) curves of the spectroscopic imaging system provided in this embodiment for each field of view at different wavelengths on the corresponding image plane. Figure 6 It can be seen that the MTF values ​​of each field of view are greater than 0.5 at 100 lp / mm, which is close to the diffraction limit. The curves are smooth, indicating that the optical system has clear and uniform imaging and the system has good imaging quality in the entire spectral range.

[0082] The snapshot imaging spectrometer spectrophotometer provided in this embodiment has an operating F-number range of 2.8 ≤ F / # ≤ 3.2; the total system length L is 30mm ≤ L ≤ 40mm. Its object-side field of view is a planar field of view, where the field of view M perpendicular to the dispersion direction is M ≥ 3mm, the field of view N in the dispersion direction is N ≥ 0.5mm, the magnification is -1×, the operating wavelength is 400nm~800nm, and the distortion is less than 0.2%.

Claims

1. A spectroscopic imaging system for a snapshot imaging spectrometer, characterized in that: The beam-splitting imaging system is an off-axis three-reflection structure; in order of light incident direction, it includes a first freeform surface mirror (1) bent towards the light incident direction, a quadratic convex diffraction grating (2) bent away from the light incident direction, a second freeform surface mirror (3) bent towards the light incident direction, a filter (4), and two photoelectric sensors (5, 6) for focusing monochromatic light of different wavelengths reflected or transmitted by the filter; the first freeform surface mirror, the quadratic convex diffraction grating, and the second freeform surface mirror are approximately concentric; the system aperture is located on the quadratic convex diffraction grating. The reflecting surface of the first freeform mirror is an XY polynomial freeform surface. In a Cartesian coordinate system with the vertex of the first freeform mirror as the origin O, the incident direction of light as the positive Z-axis, the positive Y-axis upward, and the positive X-axis inward, the expression Z1 of the reflecting surface of the first freeform mirror is: ； In the formula, c is the curvature, c=0.0259, k is the quadratic surface coefficient, k=0.005218, C2~C 20 These are the coefficients of each monomial, with a range of -4 × 10⁻⁶. -3 ≤C2≤-3×10 -3 -3×10 -6 ≤C3≤-2×10 -6 -3×10 -5 ≤C4≤-2×10 -5 -2×10 -7 ≤C5≤-1×10 -7 -2×10 -6 ≤C6≤-1×10 -6 -2×10 -8 ≤C7≤-1×10 -8 -9×10 -8 ≤C8≤-8×10 -8 4×10 -8 ≤C9≤5×10 -8 1×10 -10 ≤C 10 ≤2×10 -10 2×10 -9 ≤C 11 ≤3×10 -9 -4×10 -9 ≤C 12 ≤-3×10 -9 -4×10 -12 ≤C 13 ≤-3×10 -12 -3×10 -11 ≤C 14 ≤-2×10 -11 -6×10 -11 ≤C 15 ≤-5×10 -11 -10×10 -11 ≤C 16 ≤-9×10 -11 -2×10 -13 ≤C 17 ≤-1×10 -13 -6×10 -13 ≤C 18 ≤-5×10 -13 -7×10 -13 ≤C 19 ≤-6×10 -13 -2×10 -12 ≤C 20 ≤-1×10 -12 ; The surface shape Z2 expression of the quadric convex diffraction grating is: ； In the formula, r is the aperture radius of the quadric convex diffraction grating; k0 is the quadric coefficient, 0.35≤k0≤0.4; c0 is the curvature, -0.05≤c0≤-0.04; and the grating line density is g, 250 lines / mm≤g≤270 lines / mm. The reflecting surface of the second freeform mirror is an XY polynomial freeform surface. In a Cartesian coordinate system with the vertex of the second freeform mirror as the origin O, the incident direction of light as the positive Z-axis, the positive Y-axis upward, and the positive X-axis inward, the expression Z3 of the reflecting surface of the second freeform mirror is: ； In the formula, x and y are the coordinates of any point on the mirror surface, b is the curvature, b = -0.0229, k1 is the quadratic surface coefficient, k1 = 0.92, and B2 to B... 20 These are the coefficients of each monomial, with a range of -7 × 10⁻⁶. -3 ≤B2≤-6×10 -3 -3×10 -5 ≤B3≤-2×10 -5 -3×10 -5 ≤B4≤-2×10 -5 -2×10 -6 ≤B5≤-1×10 -6 -4×10 -6 ≤B6≤-3×10 -6 1×10 -7 ≤B7≤2×10 -7 1×10 -7 ≤B8≤2×10 -7 -2×10 -8 ≤B9≤-1×10 -8 -3×10 -9 ≤B 10 ≤-2×10 -9 -2×10 -8 ≤B 11 ≤-1×10 -8 -2×10 -8 ≤B 12 ≤-1×10 -8 2×10 -11 ≤B 13 ≤3×10 -11 -2×10 -10 ≤B 14 ≤-1×10 -10 -4×10 -10 ≤B 15 ≤-3×10 -10 -3×10 -10 ≤B 16 ≤-2×10 -10 -2×10 -12 ≤B 17 ≤-1×10 -12 -8×10 -12 ≤B 18 ≤-7×10 -12 -9×10 -12 ≤B 19 ≤-8×10 -12 -4×10 -12 ≤B 20 ≤-3×10 -12 ; The operating wavelength of the filter is 400nm to 800nm, wherein the wavelength λ1 of the reflection band is 400nm≤λ1≤600nm, and the wavelength λ2 of the transmission band is 600nm<λ2≤800nm.

2. The spectroscopic imaging system of a snapshot imaging spectrometer according to claim 1, characterized in that: Its working F-number ranges from 2.8 to 3.

2.

3. A spectroscopic imaging method for a snapshot imaging spectrometer, characterized in that... Includes the following steps: (1) After the polychromatic incident light with a wavelength of 400nm to 800nm ​​is reflected by the first free-form mirror (1) which is bent in the direction of light incident, it is incident on the convex diffraction grating (2) which is bent in the opposite direction of light incident. The reflecting surface of the first freeform mirror is an XY polynomial freeform surface. In a Cartesian coordinate system with the vertex of the first freeform mirror as the origin O, the incident direction of light as the positive Z-axis, the positive Y-axis upward, and the positive X-axis inward, the expression Z1 of the reflecting surface of the first freeform mirror is: In the formula, c is the curvature, c=0.0259, k is the quadratic surface coefficient, k=0.005218, C2~C 20 These are the coefficients of each monomial, with a range of -4 × 10⁻⁶. -3 ≤C2≤-3×10 -3 -3×10 -6 ≤C3≤-2×10 -6 -3×10 -5 ≤C4≤-2×10 -5 -2×10 -7 ≤C5≤-1×10 -7 -2×10 -6 ≤C6≤-1×10 -6 -2×10 -8 ≤C7≤-1×10 -8 -9×10 -8 ≤C8≤-8×10 -8 4×10 -8 ≤C9≤5×10 -8 1×10 -10 ≤C 10 ≤2×10 -10 2×10 -9 ≤C 11 ≤3×10 -9 -4×10 -9 ≤C 12 ≤-3×10 -9 -4×10 -12 ≤C 13 ≤-3×10 -12 -3×10 -11 ≤C 14 ≤-2×10 -11 -6×10 -11 ≤C 15 ≤-5×10 -11 -10×10 -11 ≤C 16 ≤-9×10 -11 -2×10 -13 ≤C 17 ≤-1×10 -13 -6×10 -13 ≤C 18 ≤-5×10 -13 -7×10 -13 ≤C 19 ≤-6×10 -13 -2×10 -12 ≤C 20 ≤-1×10 -12 ; The surface shape Z2 expression of the quadric convex diffraction grating is: ； In the formula, r is the aperture radius of the quadric convex diffraction grating; k0 is the quadric coefficient, 0.35≤k0≤0.4; c0 is the curvature, -0.05≤c0≤-0.04; and the grating line density is g, 250 lines / mm≤g≤270 lines / mm. (2) After being split by the quadric convex diffraction grating, each monochromatic light is reflected at different diffraction angles and incident on the second free-form surface mirror (3) which is bent towards the direction of light incidence. The reflecting surface of the second freeform mirror is an XY polynomial freeform surface. In a Cartesian coordinate system with the vertex of the second freeform mirror as the origin O, the incident direction of light as the positive Z-axis, the positive Y-axis upward, and the positive X-axis inward, the expression Z3 of the reflecting surface of the second freeform mirror is: ； In the formula, x and y are the coordinates of any point on the mirror surface, b is the curvature, b = -0.0229, k1 is the quadratic surface coefficient, k1 = 0.92, and B2 to B... 20 These are the coefficients of each monomial, with a range of -7 × 10⁻⁶. -3 ≤B2≤-6×10 -3 -3×10 -5 ≤B3≤-2×10 -5 -3×10 -5 ≤B4≤-2×10 -5 -2×10 -6 ≤B5≤-1×10 -6 -4×10 -6 ≤B6≤-3×10 -6 1×10 -7 ≤B7≤2×10 -7 1×10 -7 ≤B8≤2×10 -7 -2×10 -8 ≤B9≤-1×10 -8 -3×10 -9 ≤B 10 ≤-2×10 -9 -2×10 -8 ≤B 11 ≤-1×10 -8 -2×10 -8 ≤B 12 ≤-1×10 -8 2×10 -11 ≤B 13 ≤3×10 -11 -2×10 -10 ≤B 14 ≤-1×10 -10 -4×10 -10 ≤B 15 ≤-3×10 -10 -3×10 -10 ≤B 16 ≤-2×10 -10 -2×10 -12 ≤B 17 ≤-1×10 -12 -8×10 -12 ≤B 18 ≤-7×10 -12 -9×10 -12 ≤B 19 ≤-8×10 -12 -4×10 -12 ≤B 20 ≤-3×10 -12 ; (3) A filter (4) is used to filter several beams of monochromatic light of different wavelengths reflected by the second freeform surface mirror. The light with wavelengths of 400nm to 600nm is reflected by the filter and focused on the photoelectric sensor (5). The light with wavelengths of 600nm to 800nm ​​is transmitted through the filter and focused on another photoelectric sensor (6).

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