Eyepiece optical system and head-mounted display

1. An eyepiece optical system, wherein the optical system comprises a first lens, a second lens, a third lens, a fourth lens, and a fifth lens arranged coaxially and successively along an optical axis direction from an eye viewing side to a displayer side, wherein a focal length of the second lens is f 2 , a focal length of a lens group formed by the third lens and the fourth lens is f 34 , a focal length of the fifth lens is f 5 , a back focal length from a display of the optical system to the fifth lens proximate to a surface of the display is f d , a total system length is f w , and they satisfy following relations (1), (2), (3), and (4):

−4.00 f 2 /f w −0.50  (1);

0.35 f 34 /f w   (2);

−10.00 f 5 /f w 0.20  (3); and

0.10 f d /f w 0.50  (4).

2. The eyepiece optical system according to claim 1 , wherein the first lens, the third lens, and the fourth lens are all positive lenses, the second lens and the fifth lens are negative lenses, and the first lens, the second lens, the third lens, the fourth lens, and the fifth lens are made of glass materials or plastic materials.

3. The eyepiece optical system according to claim 2 , wherein the materials of the first lens, the second lens, and the third lens satisfy following relations (5), (6), and (7):

1.40< Nd 1 <1.90  (5);

1.40< Nd 2 <1.80  (6);

1.60< Nd 3 <1.90  (7);

wherein Nd 1 , Nd 2 , and Nd 3 are material refractive indices of the first lens, the second lens, and the third lens, respectively.

4. The eyepiece optical system according to claim 3 , wherein the materials of the first lens, the second lens, and the third lens satisfy following relations (8), (9), and (10):

40.0< Vd 1 <95.0  (8);

19.0< Vd 2 <60.0  (9);

28.0< Vd 3 <57.0  (10);

wherein Vd 1 , Vd 2 , and Vd 3 represent Abbe coefficients of the first lens, the second lens, and the third lens, respectively.

5. The eyepiece optical system according to claim 4 , wherein among the ten optical surfaces from the first optical surface to the tenth optical surface, several optical surfaces are even-order aspherical face shapes, and a formula of their face shapes is as following expression (11):

Z

=

c

⁢

r

2

1

+

1

-

(

1

+

k

)

⁢

c

2

⁢

r

2

+

α

2

⁢

r

2

+

α

4

⁢

r

4

+

α

6

⁢

r

6

+

…

⁢

.

(

11

)

6. The eyepiece optical system according to claim 4 , wherein the Abbe coefficients Vd 1 , Vd 2 , and Vd 3 of the first lens, the second lens, and the third lens further satisfy following relations (8a), (9a), and (10a):

41.5< Vd 1 <90.5  (8a);

20.0< Vd 2 <56.0  (9a); and

29.0< Vd 3 <56.0  (10a).

7. The eyepiece optical system according to claim 3 , wherein the refractive indices Nd 1 , Nd 2 , and Nd 3 of the first lens, the second lens, and the third lens further satisfy following relations (5a), (6a), and (7a):

1.50< Nd 1 <1.85  (5a);

1.45< Nd 2 <1.75  (6a); and

1.63< Nd 3 <1.87  (7a).

8. The eyepiece optical system according to claim 1 , wherein

the first lens has a first optical surface convex to an eye and a second optical surface concave to the eye;

the second lens has a third optical surface convex to the eye and a fourth optical surface concave to the eye;

the third lens has a fifth optical surface convex to the eye and a sixth optical surface convex to an image plane;

the fourth lens has a seventh optical surface convex to the eye and an eighth optical surface convex to the image plane; and

the fifth lens has a ninth optical surface concave to the image plane and a tenth optical surface concave to the eye.

9. The eyepiece optical system according to claim 8 , wherein the second optical surface on the first lens, the fifth optical surface and the sixth optical surface on the third lens, and the eighth optical surface on the fourth lens are spherical face shapes, and the other optical surfaces are all even-order aspherical face shapes.

10. The eyepiece optical system according to claim 1 , wherein a curvature radius of the optical surface of the fifth lens proximate to a human eye side is R 51 , a curvature radius of the optical surface proximate to the side of the display is R 52 , and R 51 and R 52 satisfy following relation (12):

0.5 |( R 51 +R 52 )/( R 51 −R 52 )| 4.0  (12).

11. The eyepiece optical system according to claim 10 , wherein the curvature radii R 51 and R 52 of the fifth lens further satisfy following relation (12a):

0.51 |( R 51 +R 52 )/( R 51 −R 52 )| 3.5  (12a).

12. The eyepiece optical system according to claim 1 , wherein a curvature radius of the optical surface of the second lens proximate to a human eye side is R 21 , a curvature radius of the optical surface proximate to the side of the display is R 22 , and R 21 and R 22 satisfy following relation (13):

0.8 ( R 21 +R 22 )/( R 21 −R 22 ) 6.0  (13).

13. The eyepiece optical system according to claim 12 , wherein the curvature radii R 21 and R 22 of the second lens further satisfy following relation (13a):

0.9 (( R 21 +R 22 )/( R 21 −R 22 ) 5.5  (13a).

14. The eyepiece optical system according to claim 1 , wherein the focal lengths of the second lens, the third lens, the fourth lens, and the fifth lens further satisfy following relations (1a), (2a), (3a), and (4a):

−3.60 f 2 /f w −0.85  (1a);

0.40 f 34 /f w   (2a);

−9.95 f 5 /f w 0.180  (3a); and

0.175 f d /f w 0.415  (4a).

15. A head-mounted display, comprising a miniature image display unit and an eyepiece located between human eyes and the miniature image display unit, wherein the eyepiece comprises the eyepiece optical system according to claim 1 .

16. The head-mounted display according to claim 15 , wherein a distance between the tenth optical surface on the fifth lens and the miniature image display unit is adjustable.

17. The head-mounted display according to claim 15 , wherein the head-mounted display is a double-eye head-mounted display comprising same two of the eyepiece optical systems.