Projection lens with four glass elements having spherical surfaces
A projection lens can include four lens elements, each lens element being formed from glass and including spherical or planar incident and exiting surfaces. Compared to a projection lens that uses three lens elements, the four-element projection lens has relaxed manufactured and alignment tolerances. Unlike a projection lens that uses one or more plastic elements or uses aspherical surfaces, the all-glass projection lens can be manufactured using relatively fast and inexpensive grinding and polishing techniques. One or two of the glass lens elements can optionally be formed symmetrically, so as to be reversible. One glass element can optionally be plano-convex. A right-angle prism can direct light from a video display into the four glass elements. An achromatic prism can angularly divert the optical axis by about eight degrees and can direct light out of the four glass elements into a near-eye waveguide.
1. An optical system, comprising:
a first lens element formed from a first glass having a refractive index between 1.72 and 1.85 at a wavelength of 587.6 nm and an Abbe number between 40 and 55;
a second lens element formed from second glass having a refractive index between 1.72 and 1.85 at a wavelength of 587.6 nm and an Abbe number between 38 and 55;
a third lens element formed from a third glass having a refractive index greater than 1.8 at a wavelength of 587.6 nm and an Abbe number between 20 and 24; and
a fourth lens element formed from a fourth glass having a refractive index greater than 1.85 at a wavelength of 587.6 nm and an Abbe number between 28 and 35.
2. The optical system of claim 1 , further comprising:
a projection lens having a positive total refractive power and configured to direct light in a light ray bundle from a display into a near-eye waveguide, the projection lens having an optical axis that corresponds to a center of the light ray bundle.
3. The optical system of claim 2 , wherein the projection lens comprises
the first lens element positioned along the optical axis, the first lens element having a convex spherical first incident surface facing the display and a convex spherical first exiting surface facing away from the display;
the second lens element positioned along the optical axis, the second lens element having a convex spherical second incident surface facing the first lens element and a concave spherical second exiting surface facing away from the first lens element;
the third lens element positioned along the optical axis, the third lens element having a concave spherical third incident surface facing the second lens element and a concave spherical third exiting surface facing away from the second lens element; and
the fourth lens element positioned along the optical axis, the fourth lens element having a convex spherical or planar fourth incident surface facing the third lens element and a convex spherical fourth exiting surface facing away from the third lens element.
4. The optical system of claim 1 , wherein:
a first incident surface, a first exiting surface, and the first glass define a refractive power of the first lens element to be positive and between 88% and 128% of a total refractive power;
a second incident surface, a second exiting surface, and the second glass define a refractive power of the second lens element to be positive and between 35% and 68% of the total refractive power;
a third incident surface, a third exiting surface, and the third glass define a refractive power of the third lens element to be negative and between 165% and 216% of the total refractive power; and
a fourth incident surface, a fourth exiting surface, and the fourth glass define a refractive power of the fourth lens element to be positive and between 87% and 125% of the total refractive power.
5. The optical system of claim 4 , wherein:
the refractive power of the second lens element, divided by the refractive power of the first lens element, is between 0.28 and 0.71; and
the refractive power of the fourth lens element, divided by the refractive power of the third lens element, is between −0.64 and −0.49.
6. The optical system of claim 1 , wherein:
a first incident surface, a first exiting surface, and the first glass define a refractive power of the first lens element to be positive and between 112% and 128% of a total refractive power;
a second incident surface, a second exiting surface, and the second glass define a refractive power of the second lens element to be positive and between 35% and 54% of the total refractive power;
a third incident surface, a third exiting surface, and the third glass define a refractive power of the third lens element to be negative and between 183% and 216% of the total refractive power; and
a fourth incident surface, a fourth exiting surface, and the fourth glass define a refractive power of the fourth lens element to be positive and between 91% and 125% of the total refractive power.
7. The optical system of claim 6 , wherein:
the refractive power of the second lens element, divided by the refractive power of the first lens element, is between 0.28 and 0.46; and
the refractive power of the fourth lens element, divided by the refractive power of the third lens element, is between −0.60 and −0.49.
8. The optical system of claim 6 , wherein the first incident surface and the first exiting surface have a same radius of curvature.
9. The optical system of claim 8 , wherein the third incident surface and the third exiting surface have a same radius of curvature.
10. A method for manufacturing an optical system comprising:
placing a first lens element formed from a first glass having a refractive index between 1.72 and 1.85 at a wavelength of 587.6 nm and an Abbe number between 40 and 55;
placing a second lens element formed from second glass having a refractive index between 1.72 and 1.85 at a wavelength of 587.6 nm and an Abbe number between 38 and 55;
placing a third lens element formed from a third glass having a refractive index greater than 1.8 at a wavelength of 587.6 nm and an Abbe number between 20 and 24; and
placing a fourth lens element formed from a fourth glass having a refractive index greater than 1.85 at a wavelength of 587.6 nm and an Abbe number between 28 and 35.
11. The method system of claim 10 , further comprising:
placing a projection lens having a positive total refractive power and configured to direct light in a light ray bundle from a display into a near-eye waveguide, the projection lens having an optical axis that corresponds to a center of the light ray bundle.
12. The method of claim 11 , wherein the projection lens comprises
the first lens element positioned along the optical axis, the first lens element having a convex spherical first incident surface facing the display and a convex spherical first exiting surface facing away from the display;
the second lens element positioned along the optical axis, the second lens element having a convex spherical second incident surface facing the first lens element and a concave spherical second exiting surface facing away from the first lens element;
the third lens element positioned along the optical axis, the third lens element having a concave spherical third incident surface facing the second lens element and a concave spherical third exiting surface facing away from the second lens element; and
the fourth lens element positioned along the optical axis, the fourth lens element having a convex spherical or planar fourth incident surface facing the third lens element and a convex spherical fourth exiting surface facing away from the third lens element.
13. The method of claim 10 , wherein:
a first incident surface, a first exiting surface, and the first glass define a refractive power of the first lens element to be positive and between 88% and 128% of a total refractive power;
a second incident surface, a second exiting surface, and the second glass define a refractive power of the second lens element to be positive and between 35% and 68% of the total refractive power;
a third incident surface, a third exiting surface, and the third glass define a refractive power of the third lens element to be negative and between 165% and 216% of the total refractive power; and
a fourth incident surface, a fourth exiting surface, and the fourth glass define a refractive power of the fourth lens element to be positive and between 87% and 125% of the total refractive power.
14. The method of claim 13 , wherein:
the refractive power of the second lens element, divided by the refractive power of the first lens element, is between 0.28 and 0.71; and
the refractive power of the fourth lens element, divided by the refractive power of the third lens element, is between −0.64 and −0.49.
15. The method of claim 10 , wherein:
a first incident surface, a first exiting surface, and the first glass define a refractive power of the first lens element to be positive and between 112% and 128% of a total refractive power;
a second incident surface, a second exiting surface, and the second glass define a refractive power of the second lens element to be positive and between 35% and 54% of the total refractive power;
a third incident surface, a third exiting surface, and the third glass define a refractive power of the third lens element to be negative and between 183% and 216% of the total refractive power; and
a fourth incident surface, a fourth exiting surface, and the fourth glass define a refractive power of the fourth lens element to be positive and between 91% and 125% of the total refractive power.
16. The method of claim 15 , wherein:
the refractive power of the second lens element, divided by the refractive power of the first lens element, is between 0.28 and 0.46; and
the refractive power of the fourth lens element, divided by the refractive power of the third lens element, is between −0.60 and −0.49.
17. The method of claim 15 , wherein the first incident surface and the first exiting surface have a same radius of curvature.
18. The method of claim 17 , wherein the third incident surface and the third exiting surface have a same radius of curvature.
19. An apparatus comprising:
means for placing a first lens element formed from a first glass having a refractive index between 1.72 and 1.85 at a wavelength of 587.6 nm and an Abbe number between 40 and 55;
means for placing a second lens element formed from second glass having a refractive index between 1.72 and 1.85 at a wavelength of 587.6 nm and an Abbe number between 38 and 55;
means for placing a third lens element formed from a third glass having a refractive index greater than 1.8 at a wavelength of 587.6 nm and an Abbe number between 20 and 24; and
means for placing a fourth lens element formed from a fourth glass having a refractive index greater than 1.85 at a wavelength of 587.6 nm and an Abbe number between 28 and 35.
20. The apparatus of claim 19 , further comprising:
means for placing a projection lens having a positive total refractive power and configured to direct light in a light ray bundle from a display into a near-eye waveguide, the projection lens having an optical axis that corresponds to a center of the light ray bundle.