Freeform surface optical telescope imaging system

1. A freeform surface optical telescope imaging system, comprising:

a primary mirror, a secondary mirror, a compensating mirror and a spherical mirror spaced away from each other, wherein a surface shape of each of the primary mirror and the secondary mirror is a quadric surface, the primary mirror is an aperture stop, a surface shape of the compensating mirror is a freeform surface, a surface shape of the spherical mirror is a spherical surface, a light emitted from a light source is reflected by the primary mirror, the secondary mirror, the compensating mirror, and the spherical mirror to form an image on a image plane, and an F-number of view of the freeform surface optical telescope imaging system is about 9.88.

2. The freeform surface optical telescope imaging system of claim 1 , wherein a first three-dimensional rectangular coordinates system (X,Y,Z) is defined by a location of the primary mirror, a vertex of the primary mirror is an origin of the three-dimensional rectangular coordinates system (X,Y,Z), a reflective surface of the compensating mirror is an xy polynomial freeform surface; and an xy polynomial equation is

z

⁡

(

x

,

y

)

=

c

⁡

(

x

2

+

y

2

)

1

+

1

-

(

1

+

k

)

⁢

c

2

(

x

2

+

y

2

)

+

∑

i

=

1

N

A

i

⁢

x

m

⁢

y

n

,

wherein z represents surface sag, c represents surface curvature, k represents conic constant, and Ai represents an ith term coefficient.

3. The freeform surface optical telescope imaging system of claim 2 , wherein the reflective surface of compensating mirror is a fourth-order polynomial freeform surface of xy without odd items of x; and an equation of the fourth-order polynomial freeform surface of xy is:

z

⁡

(

x

,

y

)

=

c

⁡

(

x

2

+

y

2

)

1

+

1

-

(

1

+

k

)

⁢

c

2

(

x

2

+

y

2

)

+

A

2

⁢

y

+

A

3

⁢

x

2

+

A

5

⁢

y

2

+

A

7

⁢

x

2

⁢

y

+

A

9

⁢

y

3

+

A

10

⁢

x

4

+

A

12

⁢

x

2

⁢

y

2

+

A

14

⁢

y

4

,

wherein c=0.0068854520299669, k=0.130148680498771, A 2 =0.338083764164933, A 3 =−0.00272050433148337, A 5 =−0.00262488793834259, A 7 =1.953567845767e-006, A 9 =2.22037075536239e-006, A 10 =−2.52624079993697e-008, A 12 =−5.02899069469032e-008, and A 14 =−2.16840513996516e-008.

4. The freeform surface off-axial three-mirror imaging system of claim 1 , wherein a reflecting surface of the primary mirror is an aspheric surface, and an equation of the aspheric surface is:

z

⁡

(

x

,

y

)

=

c

⁡

(

x

2

+

y

2

)

1

+

1

-

(

1

+

k

)

⁢

c

2

(

x

2

+

y

2

)

+

Ar

4

+

Br

6

+

Cr

8

+

…

,

wherein z represents surface sag, c represents surface curvature, c=−0.0020874981266865, k represents conic constant, k=13.53821544118, fourth-order coefficient A=1.65833245969156e-008, sixth-order coefficient B=5.14850429042707e-013, and eighth-order coefficient C=2.59362258572104e-017.

5. The freeform surface optical telescope imaging system of claim 1 , wherein a reflecting surface of the secondary mirror is an aspheric surface, and an equation of the aspheric surface is:

z

⁡

(

x

,

y

)

=

c

⁡

(

x

2

+

y

2

)

1

+

1

-

(

1

+

k

)

⁢

c

2

(

x

2

+

y

2

)

+

Ar

4

+

Br

6

+

Cr

8

+

…

,

wherein z represents surface sag, c represents surface curvature, c=−0.006127469485461, k represents conic constant, k=15.273223707775, fourth-order coefficient A=5.07392783277529e-007, sixth-order coefficient B=1.3788426498086e-010, and eighth-order coefficient C=7.43026486752561e-014.

6. The freeform surface optical telescope imaging system of claim 2 , wherein in the three-dimensional rectangular coordinate system (X, Y, Z), a distance between a center of the primary mirror and a center of the secondary mirror in the Z-axis direction is about 172.7688502009 mm.

7. The freeform surface optical telescope imaging system of claim 2 , wherein in the three-dimensional rectangular coordinate system (X, Y, Z), a distance between a center of the compensating mirror and a center of the secondary mirror in the Z-axis direction is about 229.89461744494 mm.

8. The freeform surface optical telescope imaging system of claim 2 , wherein in the three-dimensional rectangular coordinate system (X, Y, Z), a center coordinate of a curved surface of the spherical mirror relative to the center of the main mirror is (0, −26.98936937888, 11.17920203251).

9. The freeform surface optical telescope imaging system of claim 1 , wherein an angle between the spherical mirror and the Y-axis is about 22.85965383182°.

10. The freeform surface optical telescope imaging system of claim 2 , wherein in the three-dimensional rectangular coordinate system (X, Y, Z), a center coordinate of a curved surface of the image plane relative to the center of the main mirror is (0, −25.42232107506, 77.14934754514).

11. The freeform surface optical telescope imaging system of claim 1 , wherein an angle between the image plane and the Y axis is about 19.83794409462°.

12. The freeform surface optical telescope imaging system of claim 1 , wherein a field of view of the freeform surface optical telescope imaging system is 1.92°×1.22°.

13. The freeform surface optical telescope imaging system of claim 1 , wherein an effective focal length f of the freeform surface optical telescope imaging system is about 850 mm.

14. The freeform surface optical telescope imaging system of claim 1 , wherein an equivalent entrance pupil diameter of the freeform surface optical telescope imaging system is about 86 mm.

15. The freeform surface optical telescope imaging system of claim 1 , wherein a spherical radius of the spherical mirror is 202.107528995228 mm.