Aberration corrected optical system for near-eye displays
An optical system includes, from an image side to an object side, a first lens having a positive refractive power, a second lens having a positive refractive power, and a third lens having a negative refractive power. The first lens, the second lens, and the third lens form an optical path with the object side facing a screen and the image side adapted to provide an image from the screen to a user. In one aspect, the optical system is adapted to correct at least one of a group of aberrations including astigmatism and field curvature; or, lateral color.
1. An optical system, comprising, from an image side to an object side:
a first lens having a positive refractive power;
a second lens having a positive refractive power; and
a third lens having a negative refractive power;
wherein the first lens, the second lens, and the third lens form an optical path with the object side facing a screen and the image side adapted to provide an image from the screen to a user;
wherein the optical system is configured to satisfy at least one of:
a first pair of expressions comprising a first expression 1.0<OAL/f<1.8 and a second expression 0.0<D1/f<0.2, where OAL is distance from an image side of the first lens to a surface of the screen on the object side, D1 is air space thickness between the first lens and the second lens, and f is overall focal length of the optical systems;
a second pair of expressions comprising a first expression 0.2<BFL/f<0.9 and a second expression 0.0<D2/f<0.4, where BFL is a distance from an object side of the third lens to a surface of the screen on the object side, D2 is air space thickness between the second lens and the third lens, and f is overall focal length of the optical system;
a third pair of expressions comprising a first expression −1.0<r2/f<−0.2 and a second expression 0.5<r3/f<2.5, where r2 is a radius of curvature of a surface of the first lens facing the object side, f is overall focal length of the optical system, and r3 is a radius of curvature of a surface of the second lens facing the image side; or
a fourth pair of expressions comprising a first expression −5.0<r4/f<−0.5 and a second expression −20<r5/f<−0.5, where r4 is a radius of curvature of a surface of the second lens facing the object side, f is overall focal length of the optical system, and r5 is a radius of curvature of a surface of the third lens facing the image side.
2. The optical system of claim 1 , configured to satisfy a first expression 0.8<f1/f<2.2 and a second expression 0.8<f2/f<1.9, where f is overall focal length of the optical system, f1 is focal length of the first lens, and f2 is focal length of the second lens.
3. The optical system of claim 1 , configured to satisfy a first expression −1.0<f3/f<−0.4 and a second expression 0.4<f1/f2<2.0, where f is overall focal length of the optical system, f1 is focal length of the first lens, f2 is focal length of the second lens, and f3 is focal length of the third lens.
4. The optical system of claim 1 , configured to satisfy a first expression −3.0<f2/f3<−0.8 and a second expression |Vd2−Vd3|>24, where f2 is focal length of the second lens, f3 is focal length of the third lens, Vd2 is an Abbe number of optical material of the second lens, and V3 is an Abbe number of optical material of the third lens.
5. The optical system of claim 1 , wherein the optical system corrects at least one of:
a group of aberrations including astigmatism and field curvature; or
lateral color.
6. The optical system of claim, wherein the optical system corresponds to each of a plurality of eyepieces included in a virtual-reality head-mountable assembly, the head-mountable assembly adapted to receive a display device.
7. The optical system of claim 6 , wherein each of the plurality of eyepieces corresponds to a removable lens module.
8. The optical system of claim 6 , wherein the screen is part of a display device.
9. An optical system for producing an image, comprising:
a plurality of lenses forming an optical path having an object side facing a screen and an image side adapted to provide an image from the screen to a user, wherein the plurality of lenses corrects
lateral color to less than one milliradian by providing less than approximately ±1 diopter (dP) of user eye accommodation for a field covering at least ±45° (90°) full field of view for the screen, at the object side, having a diagonal of at least 62 mm.
10. The optical system of claim 9 , wherein the optical system corresponds to each of a plurality of eyepieces included in a virtual-reality head-mountable assembly, the head-mountable assembly adapted to receive a display device including the screen.
11. The optical system of claim 10 , wherein each of the plurality of eyepieces corresponds to a removable lens module.
12. The optical system of claim 10 , wherein the display device is a mobile phone.
13. The optical system of claim 9 , wherein:
the plurality of lenses provide an eye relief of at least 10 mm.
14. The optical system of claim 9 , wherein:
the plurality of lenses provide an eye box diameter of between approximately 12 mm and 16 mm for a pupil of the user.
15. The optical system of claim 9 , wherein the plurality of lenses comprise, from the image side to the object side:
a first lens with a positive refractive power;
a second lens with positive refractive power; and
a third lens with a negative refractive power.
16. A method of providing an optical system, comprising:
locating a first lens having a positive refractive power at a position at an image side of an optical path;
providing a second lens having a positive refractive power; and
locating a third lens having a negative refractive power at an object side of the optical path, wherein the second lens is positioned between the first lens and the third lens;
wherein the first lens, the second lens, and the third lens form the optical path with the object side facing a screen and the image side adapted to provide an image from the screen to a user;
wherein the optical system is configured to satisfy at least one of:
a first pair of expressions comprising a first expression 1.0<OAL/f<1.8 and a second expression 0.0<D1/f<0.2, where OAL is distance from an image side of the first lens to a surface of the screen on the object side, D1 is air space thickness between the first lens and the second lens, and f is overall focal length of the optical systems;
a second pair of expressions comprising a first expression 0.2<BFL/f<0.9 and a second expression 0.0<D2/f<0.4, where BFL is a distance from an object side of the third lens to a surface of the screen on the object side, D2 is air space thickness between the second lens and the third lens, and f is overall focal length of the optical system;
a third pair of expressions comprising a first expression −1.0<r2/f<−0.2 and a second expression 0.5<r3/f<2.5, where r2 is a radius of curvature of a surface of the first lens facing the object side, f is overall focal length of the optical system, and r3 is a radius of curvature of a surface of the second lens facing the image side; or
a fourth pair of expressions comprising a first expression −5.0<r4/f<−0.5 and a second expression −20<r5/f<−0.5, where r4 is a radius of curvature of a surface of the second lens facing the object side, f is overall focal length of the optical system, and r5 is a radius of curvature of a surface of the third lens facing the image side.
17. The method of claim 16 , wherein the optical system is configured to satisfy a first expression 0.8<f1/f<2.2 and a second expression 0.8<f2/f<1.9, where f is overall focal length of the optical system, f1 is focal length of the first lens, and f2 is focal length of the second lens.
18. The method of claim 16 , wherein the optical system is configured to satisfy a first expression −1.0<f3/f<−0.4 and a second expression 0.4<f1/f2<2.0, where f is overall focal length of the optical system, f1 is focal length of the first lens, f2 is focal length of the second lens, and f3 is focal length of the third lens.
19. The method of claim 16 , wherein the optical system is configured to satisfy a first expression −3.0<f2/f3<−0.8 and a second expression |Vd2−Vd3|>24, where f2 is focal length of the second lens, f3 is focal length of the third lens, Vd2 is an Abbe number of optical material of the second lens, and V3 is an Abbe number of optical material of the third lens.
20. The method of claim 16 , wherein the optical system corrects at least one of:
a group of aberrations including astigmatism and field curvature; or
lateral color.
21. The method of claim 16 , further comprising:
providing the optical system as an eyepiece included in a virtual-reality head-mountable assembly, the head-mountable assembly adapted to receive a display device including the screen.
22. The method of claim 21 , further comprising:
providing the eyepiece as part of a removable lens module.
23. The method of claim 16 , wherein a display device is a mobile phone.