Method for designing freeform concave grating imaging spectrometer

1. A method for manufacturing a freeform concave grating imaging spectrometer, comprising:

S 1 , selecting a series of light rays incident from different positions of a slit as characteristic light rays;

S 2 , calculating coordinates and normal directions of characteristic data points at intersections of the characteristic light rays and a surface of a freeform concave grating, wherein a line space of the freeform concave grating is constant;

S 3 , obtaining a freeform surface shape of the freeform concave grating by fitting, so that an initial structure is obtained;

S 4 , optimizing the initial structure; and

S 5 , manufacturing a freeform concave grating imaging spectrometer according to, parameters output in the step S 4 , wherein the freeform concave grating imaging spectrometer is a physical element; and the freeform concave grating imaging spectrometer comprises a slit, a concave grating, and an image surface.

2. The method of claim 1 , wherein a method for calculating normal direction of each characteristic data point on a surface of the freeform concave grating comprises:

S 21 ′, according to system spectral dispersion and a distance between the surface of the freeform concave grating and an image surface, calculating an angle of dispersion of a chief ray in a center of the slit;

S 22 ′, according to the angle of dispersion and spectral range, calculating a grating line distance d0; and

S 23 ′, solving R according to a formula

(

S

′

-

S

)

×

R

=

n

⁢

λ

d

⁢

G

×

R

,

wherein

n represents an order of diffraction,

λ represents a wavelength of the light,

G represents a normal direction of a grating generating surface,

R represents the normal direction of the characteristic data point on the surface of the freeform concave grating,

d represents a distance between two adjacent grating lines at a light incident point,

S represents a direction vector of an incident light at the corresponding characteristic data point on the surface of freeform concave grating, and

S′ represents a direction vector of an outgoing light at the corresponding characteristic data point on the surface of the freeform concave grating.

3. The method of claim 1 , wherein in the step S 4 , the initial system is optimized by using an optical design software.

4. The method of claim 1 , further comprising a step of processing according to parameters output in the step S 4 , so that a physical element of the freeform concave grating imaging spectrometer is obtained.

5. A method for making a freeform concave grating imaging spectrometer comprising:

S 1 , selecting a series of light rays incident from different positions of a slit as characteristic light rays;

S 2 , calculating coordinates and normal directions of characteristic data points at intersections of the characteristic light rays and a surface of a freeform concave grating, wherein a line space of the freeform concave grating is constant;

S 3 , obtaining a freeform surface shape of the freeform concave grating by fitting, so that an, initial structure is obtained; and

S 4 , optimizing the initial structure; and

S 5 , manufacturing a freeform concave grating imaging spectrometer according to parameters output in the step S 4 , wherein the freeform concave grating imaging spectrometer is a physical element; and the freeform concave grating imaging spectrometer consisting of a slit, a freeform concave grating, an image surface, and a detector; wherein the freeform concave grating is positioned to disperse and reflect a light beam irradiated from the slit, to form a reflected light beam, and the image surface is positioned to form an image from the reflected light beam irradiated from the freeform concave grating.

6. The method of claim 5 , wherein a method for calculating normal direction of each characteristic data point on a surface of the freeform concave grating comprises:

S 21 ′, according to system spectral dispersion and a distance between the surface of the freeform concave grating and an image surface, calculating an angle of dispersion of a chief ray in a center of the slit;

S 22 ′, according to the angle of dispersion and spectral range, calculating a grating line distance d0; and

S 23 ′, solving R according to a formula

(

S

′

-

S

)

×

R

=

n

⁢

λ

d

⁢

G

×

R

,

wherein

n represents an order of diffraction,

λ represents a wavelength of the light,

G represents a normal direction of a grating generating surface,

R represents the normal direction of the characteristic data point on the surface of the freeform concave grating,

d represents a distance between two adjacent grating lines at a light incident point,

S represents a direction vector of an incident light at the corresponding characteristic data point on the surface of freeform concave grating, and

S′ represents a direction vector of an outgoing light at the corresponding characteristic data point on the surface of the freeform concave grating.

7. A method for manufacturing a freeform concave grating imaging spectrometer, comprising:

S 1 , selecting a series of light rays incident from different positions of a slit as characteristic light rays;

S 2 , calculating coordinates and normal directions of characteristic data points at intersections of the characteristic light rays and a surface of a freeform concave grating, wherein a line space of the freeform concave grating is variable;

S 3 , obtaining a freeform surface shape of the freeform concave grating by fitting, so that an initial structure is obtained;

S 4 , optimizing the initial structure; and

S 5 , manufacturing a freeform concave grating imaging spectrometer according to parameters output in the step S 4 , wherein the freeform concave grating imaging spectrometer is a physical element; and the freeform concave grating imaging spectrometer comprises a slit, a concave grating, and an image surface.

8. The method of claim 7 , wherein a method for calculating the normal direction of each characteristic data point on a surface of the freeform concave grating comprises:

S 21 , setting a surface shape of the freeform concave grating to a spherical surface, wherein an intersection point of the characteristic light and the spherical surface is the characteristic data point, and the normal direction R of the spherical surface at each characteristic data point is known; in formula

(

S

′

-

S

)

×

R

=

n

⁢

λ

d

⁢

G

×

R

,

wherein

n represents an order of diffraction,

λ represents a wavelength of the light,

G represents a normal direction of a grating generating surface,

R represents the normal direction of the characteristic data point on the surface of the freeform concave grating,

d represents a distance between two adjacent grating lines at a light incident point,

S represents a direction vector of an incident light at the corresponding characteristic data. point on the surface of freeform concave grating, and

S′ represents a direction vector of an outgoing light at the corresponding characteristic data point on the surface of the freeform concave grating;

except for d, all are known quantities, so that grating line distance d at the characteristic data point is solved; after the grating line distances at all the characteristic data points are solved, accordingto formula d(x,y)=d 0 +d 1 y+d 2 y 2 +d 3 y 3 +L, a function d(y) is obtained by fitting, wherein the function d(y) represents grating line distance varied with the change of the coordinate y; and

S 22 , according to the formula

(

S

′

-

S

)

×

R

=

n

⁢

λ

d

⁢

G

×

R

,

solving the normal direction R of the characteristic data point on the freeform concave grating, wherein

n represents an order of diffraction;

λ represents a wavelength of the light,

G represents a normal direction of a grating generating surface,

R represents the normal direction of the characteristic data point on the surface of the freeform concave grating,

d represents a distance between two adjacent grating lines at a light incident point,

S represents a direction vector of an incident light at the corresponding characteristic data point on the surface of freeform concave grating, and

S′ represents a direction vector of an outgoing light at the corresponding characteristic data point on the surface of the freeform concave grating.

9. The method of claim 8 , wherein the step S 3 further comprises:

S 31 , fixing obtained freeform surface shape, repeating the step S 21 , and calculating a variation function of a new grating line space;

S 32 , repeating the step S 22 , to obtain a corresponding new freeform surface shape; and

S 33 , repeating the steps S 31 and S 32 .

10. The method of claim 7 , wherein in the step S 4 , the initial system is optimized by using an optical design software.

11. The method of claim 7 , further comprising a step of processing according to parameters output in the step S 4 , so that a physical element of the freeform concave grating imaging spectrometer is obtained.