CN114280764B - Free-form surface prism-based large-view-field spectroscopic imaging method and system - Google Patents
Free-form surface prism-based large-view-field spectroscopic imaging method and system Download PDFInfo
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Abstract
The invention relates to a large-view-field spectroscopic imaging method and a system based on a free-form surface prism. The light reaches an incident light reflection area of the free-form surface reflector through an incident slit to be reflected, and the reflected light is subjected to four-time dispersion treatment in a curved prism spectroscope group through a folded light path to realize light splitting and aberration balance, so that the nonlinear dispersion corrected divergent monochromatic light rays with different fields of view and wavelengths are obtained; the light beam is incident on the light-splitting reflection area of the free-form surface reflector, reflected and converged at the image plane. The light splitting part of the light splitting imaging system provided by the invention adopts a structure that light rays pass through the curved prism group twice, so that the light energy utilization rate is high, and the dispersion linearity is good; the system utilizes a concentric optical structure and prism dispersion to realize spectral imaging with large field of view, high resolution and high light energy utilization rate, has simple and compact structure, is easy to assemble and tune, and has wide application prospect.
Description
Technical Field
The invention relates to the technical field of spectrometers, in particular to a large-view-field spectroscopic imaging method and a system based on a free-form surface prism.
Background
The spectrum imaging technology combines the spectrum and the imaging technology, realizes the simultaneous acquisition of two-dimensional image information and one-dimensional spectrum information of a target scene, forms a three-dimensional data cube, and analyzes and processes the acquired spectrum information. From satellite image analysis to food safety detection, the application of the spectrum imaging technology is extremely wide, and with the development of a new application background, a new working environment has higher requirements on indexes such as field of view, signal to noise ratio, resolution and the like of a spectrum imaging system.
The spectroscopic technology is the core of the spectrometer system and determines the basic performance of the imaging spectrometer, wherein the spectrometer system designed by taking the grating and the prism as the spectroscopic element is most. The traditional Offner spectrometer uses a convex grating as a light-splitting element thereof, has good imaging performance, but the convex grating is difficult to manufacture and expensive, and the grating generally only uses a certain level of spectrum, so that the light energy utilization rate is low, and meanwhile, the defects of stray light, spectrum overlapping, ghost images and the like still exist. Before the invention is made, chinese patent No. 110319932A discloses a curved prism dispersion type imaging optical system based on an Offner relay structure, but the system has small numerical aperture and small view field, and the system introduces too many prisms and adopts a mode of separating a main reflector, so that the difficulty of system assembly and calibration is increased.
In a concentric optical system, the symmetry of the system is destroyed due to the addition of a dispersion element, a larger astigmatic aberration system exists, and the longer the slit is, the more difficult the aberration correction is, the method for separating the main reflector and the third reflector is adopted in the prior art, and the optimization variable is added, however, the method improves the complexity of the optical structure, and the system is difficult to assemble and calibrate.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a large-view-field spectral imaging system with high light energy utilization rate, high spectral resolution, simple and compact structure and easy tooling adjustment and an imaging method thereof.
The technical scheme for realizing the purpose of the invention is to provide a large-view-field spectroscopic imaging system based on a free-form surface prism; the optical path of the system is in a symmetrical structure and comprises an incident slit, a reflecting mirror and a curved prism spectroscope group which are in an approximately concentric structure; the reflecting mirror is a free-form surface reflecting mirror, and the curved surface of the reflecting mirror is bent to the light incidence direction and comprises an incidence light reflecting area and a light splitting reflecting area; the curved surface prism spectroscope group comprises a curved surface prism and a free-form surface prism, the vertex angles of the two prisms are oppositely arranged, and the curved surfaces of the two prisms are bent to the incident direction of light; refractive index n of material of the curved prism 1 The value range of (2) is 1.7-n 1 The Abbe number v is less than or equal to 1.9 1 The value range of (2) is 25.44 v or less 1 Not more than 32.15; refractive index n of the material of the free-form surface prism 2 The value range of (2) is 1.4-n 2 The Abbe number v is less than or equal to 1.6 2 The value range of (2) is 66.2 v or less 2 Less than or equal to 68.2; the reflecting surface of the free-form surface prism is plated with a high-reflection film, and the systemIs disposed on the reflecting surface of the freeform prism.
The technical scheme of the invention also comprises a large-view-field spectroscopic imaging method based on the freeform prism, which comprises the following steps:
(1) After passing through the entrance slit, the light rays are converged by the incident light reflection area of the free-form surface reflector;
the curved surface of the free-form surface reflector is bent to the light incidence direction and comprises an incident light reflection area and a light splitting reflection area;
(2) The converging light obtained in the step (1) is incident into a curved prism spectroscope group, and is subjected to four-time dispersion treatment by a folding light path in the curved prism spectroscope group, so that light splitting and aberration balancing are realized, and the diverging monochromatic light with different fields of view and wavelengths for nonlinear dispersion correction is obtained;
the curved surface prism spectroscope group and the free-form surface reflecting mirror are in an approximate concentric structure, the curved surface prism spectroscope group comprises a curved surface prism and a free-form surface prism, the vertex angles of the two prisms are oppositely arranged, and the curved surfaces of the two prisms are bent to the incident direction of light; refractive index n of material of the curved prism 1 The value range of (2) is 1.7-n 1 The Abbe number v is less than or equal to 1.9 1 The value range of (2) is 25.44 v or less 1 Not more than 32.15; refractive index n of the material of the free-form surface prism 2 The value range of (2) is 1.4-n 2 The Abbe number v is less than or equal to 1.6 2 The value range of (2) is 66.2 v or less 2 Less than or equal to 68.2; the reflection surface of the free-form surface prism is plated with a high-reflection film, and the aperture diaphragm of the system is arranged on the reflection surface of the free-form surface prism;
(3) And (3) incidence of the divergent monochromatic light rays with different fields of view and wavelengths obtained in the step (2) to a beam splitting reflection area of the free-form surface reflector, and convergence imaging at an image plane after aberration balancing.
In the technical scheme of the invention, the reflecting surface of the free-form surface reflecting mirror is an XY polynomial free-form surface, a coordinate system in which the reflecting surface is positioned is a Cartesian space rectangular coordinate system constructed by taking the vertex of the free-form surface reflecting mirror as an origin O, the incident direction of light is the positive direction of a Z axis, the positive direction of the Y axis is upward, the positive direction of the X axis is outward, and the equation of the XY polynomial free-form surface in the coordinate system is as follows:
wherein,is the radius; c is the curvature, c= -4.63 x 10 -3 The method comprises the steps of carrying out a first treatment on the surface of the k is a quadric coefficient, k=0.243; />～/>The coefficients of the individual formulas are respectively within the value range of 0.197 +.>≤0.199， -1.725≤/>≤-1.723，-1.688≤/>≤-1.686，0.061≤/>≤0.063，0.018≤/>≤0.021，0.077≤/>≤0.079，0.173≤≤0.175，-0.160≤/>≤-0.158，-3.07×10 -3 ≤/>≤-3.04×10 -3 ，0.010≤/>≤0.014，0.125≤/>≤0.128。
The reflection surface of the free-form surface prism is an XY polynomial free-form surface, the coordinate system is a Cartesian space rectangular coordinate system constructed by taking the top point of the free-form surface prism as an origin O, the light incidence direction is a Z-axis positive direction, a Y-axis positive direction is upward, an X-axis positive direction is outward, and the equation of the XY polynomial free-form surface in the coordinate system is as follows:
wherein,is the radius; c is curvature, c= -0.011; k is a quadric coefficient, k=2.36×10 -3 ；/>～/>The coefficients of the individual formulas are respectively within the value range of 0.010 less than or equal to ∈0>≤0.012， -5.31×10 -5 ≤/>≤-4.91×10 -5 ，-1.2×10 -4 ≤/>≤-1.0×10 -4 ，-4.51×10 -3 ≤/>≤-4.48×10 -3 ，3.42×10 -3 ≤/>≤3.44×10 -3 ，7.635×10 -4 ≤/>≤7.640×10 -4 ，2.11×10 -3 ≤/>≤2.13×10 -3 ，-3.3×10 -3 ≤≤-3.1×10 -3 ，3.95×10 -3 ≤/>≤3.97×10 -3 ，-2.93×10 -4 ≤/>≤-2.88×10 -4 ，8.85×10 -4 ≤/>≤8.89×10 -4 。
The principle of the invention is as follows: the light reaches the free-form surface reflector through the entrance slit to be reflected; after passing through the first curved prism and the second free-form surface prism, the reflected light is reflected by the rear surface of the free-form surface prism, and passes through the free-form surface prism and the curved prism again respectively, so that the light splitting and aberration balancing effects of the curved prism are achieved; the light beam after dispersion and light splitting is incident on the free-form surface reflecting mirror again, the reflecting mirror performs aberration compensation and correction on light with different wavelengths and different fields of view, and meanwhile, the light beam is converged at the image plane to obtain an image with a large field of view, high resolution and high light energy utilization rate.
According to the invention, the dispersion value of the prism in the specified band interval is obtained according to the relation between the refractive index of the material and the wavelength, a uniform dispersion ideal expression of the glass pair is established, the total dispersion value of the vertex angle size of the prism group is obtained, the prism combination in the applicable range is selected as a light splitting element of the imaging spectrometer, and the dispersion nonlinearity is effectively corrected. Flint glass and quartz glass were selected from a common glass warehouse, and the rear surface of the flint glass was coated with a reflective film. As a convex mirror in an Offner system, reduces the system volume and mass.
The invention utilizes the two curved prisms to form the light-splitting part of the system, reduces the nonlinearity of chromatic dispersion to a certain extent, introduces a free curved surface at the rear surface of the second prism, expands the optimization degree of freedom and improves the aberration balance capability of the system. The free-form surface is non-rotationally symmetrical, and compared with a standard spherical surface and an aspherical surface, the free-form surface has more remarkable aberration compensation and correction capability and the capability of improving the view field and the spectral resolution of the system.
The prism group adopted by the invention consists of two curved prisms with different materials, and nonlinear dispersion correction is realized through reasonable selection of glass materials; four-time dispersion is realized by twice passing of incident light through the prism group, and the number of the prisms and the volume of the system are reduced under the same design index, so that the structure is more compact. According to the invention, by introducing the free-form surface and the curved surface prism, only two prisms and one reflecting mirror are utilized to lift the view field to 70-80 mm, and the light rays pass through the prism group twice, so that the dispersion rate is improved. Because the curved prism has the functions of dispersion and focusing, but loses symmetry in the meridian direction, astigmatism is the inherent aberration of the curved prism, and the introduced light splitting element also breaks the symmetry of the Offner structure to have larger astigmatism, so that free curved surfaces are introduced at two positions of the system, and the light of each wavelength and each view field is balanced and the aberration is corrected.
Compared with the prior art, the invention has the beneficial effects that:
1. the invention introduces the free-form surface prism, only uses two surface prisms with different materials to form a system beam splitting part, and makes the light beam pass through the surface prism group twice, thereby ensuring high light energy utilization rate and simultaneously effectively inhibiting dispersion nonlinearity; and a reflecting film is plated on the rear surface of the free-form surface prism, so that the volume and the mass of the system are reduced.
2. The invention sets the incident light reflection and the light splitting reflection in different areas of the same free-form surface reflecting mirror, thereby facilitating the adjustment; the free curved surface and the curved prism are combined, astigmatism introduced due to the fact that the radial direction of the curved prism is out of symmetry is effectively balanced, meanwhile, distortion improvement is obvious, spectral line bending is controlled within 6 mu m, spectral line bending is controlled within 0.5 mu m, and spectral calibration and later-stage image processing are facilitated.
3. The invention uses the advantages of concentric optical system and prism dispersion, has large numerical aperture, high incident light flux and few introduced optical elements, is only composed of two curved prisms and a reflecting mirror, has simple and compact structure, is easy to adjust, and has practical application value.
Drawings
Fig. 1 is a schematic structural diagram of a spectroscopic imaging system according to an embodiment of the present invention;
FIG. 2 is a schematic diagram showing the refractive index of glass according to the wavelength in the embodiment of the present invention;
FIG. 3 is a schematic diagram of a curved prism beam splitter according to an embodiment of the present invention;
FIG. 4 is a plot of the RMS radius of a focused spot in a full field of view full operating band of a spectroscopic imaging system provided by an embodiment of the present invention;
FIG. 5 is a graph of the transfer function curve MTF of a spectroscopic imaging system provided by an embodiment of the present invention;
in the figure, 1. Entrance slit; 2. a free-form surface mirror; 3. a curved prism; 4. a free-form surface prism; 41. a free-form surface prism rear surface (reflecting surface); 5. an image plane.
Detailed Description
Specific embodiments of the present invention are further described below with reference to the accompanying drawings and examples.
Embodiment one:
the technical scheme of the embodiment is to provide a large-view-field spectroscopic imaging system based on a free-form surface prism and an imaging method thereof. The F number of the optical system is F/# = 5; the total length S of the incident slit is S=70 mm, and the working wavelength is 400-800 nm.
Referring to fig. 1, which is a schematic structural diagram of a spectroscopic imaging system provided in this embodiment, an optical path of the system is in a symmetrical structure, and according to a light incident direction, optical elements are sequentially as follows: the system comprises an entrance slit 1, a free-form surface reflector 2, a curved surface prism spectroscope group consisting of a curved surface prism 3 and a free-form surface prism 4 and an image surface 5; the free-form surface reflecting mirror and the surface prism spectroscope group are in an approximate concentric structure; the reflection curved surface of the free-form surface reflector is bent to the light incidence direction and comprises an incident light reflection area and a light splitting reflection area; in a curved surface prism spectroscope group formed by a curved surface prism and a free surface prism, the vertex angles of the two prisms are oppositely arranged, the curved surfaces of the two prisms are bent to the incident direction of light, the rear surface 41 of the free surface prism is a reflecting surface plated with a high-reflection film, and the aperture diaphragm of the system is arranged on the reflecting surface of the free surface prism.
In this embodiment, the reflecting surface of the free-form surface reflecting mirror is an XY polynomial free-form surface, the coordinate system in which the XY polynomial free-form surface reflecting mirror is located is a cartesian space rectangular coordinate system constructed by using the vertex of the free-form surface reflecting mirror as the origin O, the light incident direction is the positive Z-axis direction, the positive Y-axis direction is upward, and the positive X-axis direction is outward, and the equation of the XY polynomial free-form surface in the coordinate system is:
wherein,is the radius; c is the curvature, c= -4.63 x 10 -3 The method comprises the steps of carrying out a first treatment on the surface of the k is a quadric coefficient, k=0.243; />～/>The coefficients of the individual expressions are respectively: />=0.198， />=-1.724，/>=-1.687，/>=0.062，/>=0.02，/>=0.078，/>=0.174，/>=-0.159，/>=-3.05×10 -3 ，/>=0.012，/>=0.127。
In this embodiment, the reflecting surface of the freeform prism is an XY polynomial freeform surface, the coordinate system in which the reflecting surface is located is a cartesian space rectangular coordinate system constructed by using the vertex of the freeform prism as the origin O, the light incident direction is the positive Z-axis direction, the positive Y-axis direction is upward, the positive X-axis direction is outward, and the equation of the XY polynomial freeform surface in the coordinate system is:
where c is the curvature, c= -0.011; k is a quadric coefficient, k=2.36×10 -3 ；Is the radius; />～/>The coefficients of the individual expressions are respectively: />=0.011， />=-5.11×10 -5 ， />=-1.11×10 -4 ， />=-4.49×10 -3 ， />=3.43×10 -3 ， />=7.638×10 -4 ， />=2.12×10 -3 ， />=-3.2×10 -3 ， />=3.958×10 -3 ， />=-2.912×10 -4 ， />=8.872×10 -4 。
When the spectral imaging system provided by the embodiment images, light reaches an incident light reflection area of the free-form surface reflector 2 through the incident slit 1 to be reflected; the reflected light sequentially passes through the curved prism 3 and the free-form surface prism 4 of the curved prism spectroscope group, is reflected by the rear surface 41 of the free-form surface prism, and sequentially passes through the free-form surface prism and the curved prism, so that the light energy utilization rate is high, the dispersion linearity is good, and the dispersion and light splitting effect is achieved; the light beam after dispersion and light splitting is incident on the free-form surface reflector again, and the incident light with different wavelengths is converged at the image plane 5 after being reflected by the light splitting reflection area of the free-form surface reflector.
Referring to fig. 2, which is a schematic diagram of the refractive index of the glass according to the present embodiment, the essential disadvantage of the prism dispersion system is the non-uniformity of dispersion, which is determined by the refractive index of the prism optical material. When using a prism as the imaging system of the spectroscopic element, the spectral sampling interval is wavelength-dependent. Let the dispersion ratio of the prism beThenIt represents the degree of change in refractive index of a material with wavelength. If the wedge angle of a certain optical glass prism is +.>: the dispersion value of the dispersion in the whole wave band is A, and the dispersion value in the short wave direction is less than the band interval +.>The dispersion value in the optical fiber is B, and the dispersion value at the same wavelength interval in the long-wavelength direction is C, and the following are:
in general, the refractive index of the glass material decreases with increasing wavelength, and thus the brackets in the above three formulas are positive values. To correct for dispersion non-uniformity, prisms of another material are taken to be opposite vertex angles, i.e. negative values are introduced。
Referring to fig. 3, a schematic structural diagram of a beam-splitting prism pair according to the present embodiment is shown, where the wedge angle of the first prism isThe wedge angle of the second prism is +.>The first prism has a corresponding chromatic dispersion value ofA 1 、B 1 AndC 1 the second prism corresponds to a dispersion value ofA 2 、B 2 AndC 2 the uniform dispersion equation for a glass pair is expressed as follows:
the total dispersion value of the prism pair is expressed as:
and flint glass and quartz glass are screened from a common glass warehouse to serve as prism pairs, and a prism combination which has a good effect in the application range and is easy to process is selected to serve as a light splitting element of an imaging system, so that nonlinear dispersion is effectively corrected. The back surface of flint glass is directly coated with a reflecting film, so that light beams pass through the curved prism group twice, the volume and the quality of the system are reduced, the symmetry of the system is kept, and meanwhile, higher freedom degree is provided for aberration correction in optical design.
The parameters of the optical elements of this example are shown in table 1.
Table 1:
in the present embodiment, the refractive index n of the material of the curved prism 3 1 =1.755, abbe number v 1 =27.58; refractive index n of material of free-form surface prism 4 2 Abbe number v=1.458 2 =67.82。
The imaging method of the spectroscopic imaging system provided by the embodiment comprises the following steps:
(1) The light rays are converged by the incident light reflection area of the free-form surface reflector 2 after passing through the incident slit 1;
(2) The converging light obtained in the step (1) is incident into a curved prism spectroscope group consisting of a curved prism 3 and a free curved prism 4, and is subjected to four-time dispersion treatment by a folding light path in the curved prism spectroscope group, so that light splitting and aberration balancing are realized, and the diverging monochromatic light with different fields of view and wavelengths for nonlinear dispersion correction is obtained;
(3) And (3) incidence of the divergent monochromatic light rays with different fields of view and wavelengths obtained in the step (2) to a light splitting reflection area of the free-form surface reflector, and convergence imaging at an image plane 5 after aberration balancing.
The performance parameters of the spectroscopic imaging system provided in this embodiment are shown in table 2.
Table 2:
| spectral range (nm) | 400～800 |
| Numerical aperture | 0.1 |
| Image plane dispersion width (mm) | 2 |
| Slit length (mm) | 70 |
| Short wavelength spectral resolution (nm) | ＜1 |
| Long wavelength spectral resolution (nm) | ＜8 |
| Spectral channel number | 200 |
| Spectral line bending (mum) | ＜6 |
| Band bending (mum) | ＜0.5 |
Referring to fig. 4, it is a graph of RMS radius of a focused spot in a full-field operating band of the spectroscopic imaging system provided in this embodiment, where curve (a) is RMS radius of the full-field full-operating band, and curve (b) is RMS radius of the full-operating band at the diffraction limit. As can be seen from fig. 4, in the full field of view full operating band, the RMS radius of the system is less than 5.2 μm, approaching the diffraction limit RMS radius, and the energy is concentrated, meeting the usage requirements.
Referring to fig. 5, a graph of MTF of a transfer function on an image plane corresponding to each field of view of the spectroscopic imaging system provided in the present embodiment is shown; in the figures, (a) and (b) correspond to the MTF curves of all the field of view transfer functions of the imaging spectrometer provided in the present embodiment on the image planes with wavelengths of 0.4 μm, 0.6 μm and 0.8 μm, respectively. As can be obtained from fig. 3, the optical transfer function of the full view field of the working wave band from 0.4 μm to 0.8 μm at 70lp/mm is larger than 0.3, the diffraction limit is approached, the curve is smooth and compact, the imaging of the system is clear and uniform, and the system has good imaging quality in the full wave band and the full view field.
The large-view-field spectroscopic imaging system adopting the free-form surface prism, which is provided by the technical scheme of the invention, is only composed of three optical elements, and improves the light energy utilization rate and the spectral resolution by introducing the free-form surface and curved surface prism to balance and correct the system aberration. The system adopts a concentric structure, is easy to correct distortion, and has the advantages of flat image field, small volume, light weight and the like; meanwhile, a prism group in the application range is screened to be used as a system light splitting element, chromatic dispersion nonlinearity is corrected, and spectrum calibration is facilitated. The system integrates a free-form surface and a curved prism, realizes aberration balance, particularly astigmatism, inhibits dispersion nonlinearity, has the characteristics of large field of view, high light energy utilization rate and high resolution, has few optical elements and small volume, and has wide application prospect.
Claims (2)
1. A large view field spectroscopic imaging system based on free curved prismThe method is characterized in that: the optical path of the system is in a symmetrical structure and comprises an incident slit (1), a reflecting mirror with an approximate concentric structure and a curved prism spectroscope group; the reflecting mirror is a free-form surface reflecting mirror (2), and the curved surface of the reflecting mirror is bent to the direction of an incident slit of the system and comprises an incident light reflecting area and a light splitting reflecting area; the curved surface prism spectroscope group comprises a curved surface prism (3) and a free-form surface prism (4), the vertex angles of the two prisms are oppositely arranged, and the curved surfaces of the two prisms are bent to the direction of an incident slit of the system; refractive index n of material of the curved prism 1 The value range of (2) is 1.7-n 1 The Abbe number v is less than or equal to 1.9 1 The value range of (2) is 25.44 v or less 1 Not more than 32.15; refractive index n of the material of the free-form surface prism 2 The value range of (2) is 1.4-n 2 The Abbe number v is less than or equal to 1.6 2 The value range of (2) is 66.2 v or less 2 Less than or equal to 68.2; the reflection surface (41) of the free-form surface prism is plated with a high-reflection film, and the aperture diaphragm of the system is arranged on the reflection surface of the free-form surface prism;
the reflection surface of the free-form surface reflecting mirror is an XY polynomial free-form surface, a coordinate system of the free-form surface reflecting mirror is a Cartesian space rectangular coordinate system constructed by taking the top point of the free-form surface reflecting mirror as an origin O, the incidence direction of light is a Z-axis positive direction, a Y-axis positive direction is upward, an X-axis positive direction is outward, and an equation of the XY polynomial free-form surface in the coordinate system is as follows:
wherein,is the radius; c is the curvature, c= -4.63 x 10 -3 The method comprises the steps of carrying out a first treatment on the surface of the k is a quadric coefficient, k=0.243; a, a 1 ～a 11 The values of the coefficients are respectively the coefficients of the single formulas, and the value range is 0.197 less than or equal to a 1 ≤0.199，-1.725≤a 2 ≤-1.723，-1.688≤a 3 ≤-1.686，0.061≤a 4 ≤0.063，0.018≤a 5 ≤0.021，0.077≤a 6 ≤0.079，0.173≤a 7 ≤0.175，-0.160≤a 8 ≤-0.158，-3.07×10 -3 ≤a 9 ≤-3.04×10 -3 ，0.010≤a 10 ≤0.014，0.125≤a 11 ≤0.128；
Or the reflecting surface of the free-form surface prism is an XY polynomial free-form surface, the coordinate system is a Cartesian space rectangular coordinate system constructed by taking the vertex of the free-form surface prism as an origin O, the light incidence direction is a Z-axis positive direction, a Y-axis positive direction is upward, an X-axis positive direction is outward, and the equation of the XY polynomial free-form surface in the coordinate system is as follows:
wherein,is the radius; c is curvature, c= -0.011; k is a quadric coefficient, k=2.36×10 -3 ；a 1 ～a 11 The values of the coefficients are respectively the coefficients of the single formulas, and the value range is 0.010 less than or equal to a 1 ≤0.012，-5.31×10 -5 ≤a 2 ≤-4.91×10 -5 ，-1.2×10 -4 ≤a 3 ≤-1.0×10 -4 ，-4.51×10 -3 ≤a 4 ≤-4.48×10 -3 ，3.42×10 -3 ≤a 5 ≤3.44×10 -3 ，7.635×10 -4 ≤a 6 ≤7.640×10 -4 ，2.11×10 -3 ≤a 7 ≤2.13×10 -3 ，-3.3×10 -3 ≤a 8 ≤-3.1×10 -3 ，3.95×10 -3 ≤a 9 ≤3.97×10 -3 ，-2.93×10 -4 ≤a 10 ≤-2.88×10 -4 ，8.85×10 -4 ≤a 11 ≤8.89×10 -4 。
2. A large-view-field spectroscopic imaging method based on a freeform prism is characterized by comprising the following steps:
(1) After passing through the entrance slit (1), the light rays are converged by an incident light reflection area of the free-form surface reflector (2);
the curved surface of the free-form surface reflector is bent to the direction of an incident slit of the system, and comprises an incident light reflection area and a light splitting reflection area;
(2) The converging light obtained in the step (1) is incident into a curved prism spectroscope group, and is subjected to four-time dispersion treatment by a folding light path in the curved prism spectroscope group, so that light splitting and aberration balancing are realized, and the diverging monochromatic light with different fields of view and wavelengths for nonlinear dispersion correction is obtained;
the curved surface prism spectroscope group and the free-form surface reflecting mirror are in an approximate concentric structure, the curved surface prism spectroscope group comprises a curved surface prism (3) and a free-form surface prism (4), the vertex angles of the two prisms are oppositely arranged, and the curved surfaces of the two prisms are bent to the direction of an incident slit of the system; refractive index n of material of the curved prism 1 The value range of (2) is 1.7-n 1 The Abbe number v is less than or equal to 1.9 1 The value range of (2) is 25.44 v or less 1 Not more than 32.15; refractive index n of the material of the free-form surface prism 2 The value range of (2) is 1.4-n 2 The Abbe number v is less than or equal to 1.6 2 The value range of (2) is 66.2 v or less 2 Less than or equal to 68.2; the reflection surface (41) of the free-form surface prism is plated with a high-reflection film, and the aperture diaphragm of the system is arranged on the reflection surface of the free-form surface prism;
(3) The divergent monochromatic light rays with different fields of view and wavelengths obtained in the step (2) are incident into a beam splitting reflection area of a free-form surface reflector, and are focused and imaged at an image plane after aberration balance;
the reflection surface of the free-form surface reflecting mirror is an XY polynomial free-form surface, a coordinate system of the free-form surface reflecting mirror is a Cartesian space rectangular coordinate system constructed by taking the top point of the free-form surface reflecting mirror as an origin O, the incidence direction of light is a Z-axis positive direction, a Y-axis positive direction is upward, an X-axis positive direction is outward, and an equation of the XY polynomial free-form surface in the coordinate system is as follows:
wherein,is the radius; c is the curvature, c= -4.63 x 10 -3 The method comprises the steps of carrying out a first treatment on the surface of the k is a quadric coefficient, k=0.243; a, a 1 ～a 11 The values of the coefficients are respectively the coefficients of the single formulas, and the value range is 0.197 less than or equal to a 1 ≤0.199，-1.725≤a 2 ≤-1.723，-1.688≤a 3 ≤-1.686，0.061≤a 4 ≤0.063，0.018≤a 5 ≤0.021，0.077≤a 6 ≤0.079，0.173≤a 7 ≤0.175，-0.160≤a 8 ≤-0.158，-3.07×10 -3 ≤a 9 ≤-3.04×10 -3 ，0.010≤a 10 ≤0.014，0.125≤a 11 ≤0.128；
Or the reflecting surface of the free-form surface prism is an XY polynomial free-form surface, the coordinate system is a Cartesian space rectangular coordinate system constructed by taking the vertex of the free-form surface prism as an origin O, the light incidence direction is a Z-axis positive direction, a Y-axis positive direction is upward, an X-axis positive direction is outward, and the equation of the XY polynomial free-form surface in the coordinate system is as follows:
wherein,is the radius; c is curvature, c= -0.011; k is a quadric coefficient, k=2.36×10 -3 ；a 1 ～a 11 The values of the coefficients are respectively the coefficients of the single formulas, and the value range is 0.010 less than or equal to a 1 ≤0.012，-5.31×10 -5 ≤a 2 ≤-4.91×10 -5 ，-1.2×10 -4 ≤a 3 ≤-1.0×10 -4 ，-4.51×10 -3 ≤a 4 ≤-4.48×10 -3 ，3.42×10 -3 ≤a 5 ≤3.44×10 -3 ，7.635×10 -4 ≤a 6 ≤7.640×10 -4 ，2.11×10 -3 ≤a 7 ≤2.13×10 -3 ，-3.3×10 -3 ≤a 8 ≤-3.1×10 -3 ，3.95×10 -3 ≤a 9 ≤3.97×10 -3 ，-2.93×10 -4 ≤a 10 ≤-2.88×10 -4 ，8.85×10 -4 ≤a 11 ≤8.89×10 -4 。
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