Spatially varying skew mirrors
A skew mirror is an optical reflective device whose reflective axis forms a non-zero angle with the surface normal. A spatially varying skew mirror is a skew mirror whose reflective axes vary as a function of lateral position. If a spatially varying skew mirror was subdivided into many pieces, some or all of the many pieces could have a reflective axis that points in a different direction. In some variations, a spatially varying skew mirror can act as a focusing mirror that focuses incident light. A spatially varying skew mirror can be made by recording interference patterns between a phase-modulated writing beam and another writing beam or by recording interference patterns between planar wavefronts in a curved holographic recording medium that is later bent or warped.
1. A holographic optical element comprising:
a grating structure in a grating medium, wherein the grating structure is configured to reflect an incident collimated beam about spatially varying skew axes to form a reflected beam having a reflected wavefront characterized by a non-zero third-order or higher Zernike coefficient, the spatially varying skew axes forming non-zero angles with a surface normal of the surface of the grating medium in at least some spatial locations and the grating structure comprising:
a first grating disposed at a first location in the grating medium and characterized by a first grating vector having a first length and pointing in a first direction, and
a second grating disposed at the first location in the grating medium and characterized by a second grating vector having a second length and pointing in the first direction, the second length being different than the first length.
2. The holographic optical element of claim 1 , wherein the spatially varying skew axes have orientations that vary smoothly as a function of position within the grating medium.
3. The holographic optical element of claim 1 , wherein the grating structure is configured to focus the reflected beam to a virtual focal point.
4. The holographic optical element of claim 3 , wherein the virtual focal point is 1 meter to 10 meters from the grating structure.
5. The holographic optical element of claim 1 , wherein the grating structure is configured to focus the reflected beam to a real focal point.
6. The holographic optical element of claim 5 , wherein the real focal point is 1 meter to 10 meters from the grating structure.
7. The holographic optical element defined in claim 1 , wherein the grating medium is located within a waveguide.
8. The holographic optical element defined in claim 7 , wherein the waveguide is located within a head-mounted display.
9. A holographic optical element comprising:
a grating structure residing in a grating medium, wherein the grating structure is configured to reflect an incident collimated beam about spatially varying skew axes to form a reflected beam having a reflected wavefront characterized by a non-zero third-order or higher Zernike coefficient, the spatially varying skew axes forming non-zero angles with a surface normal of the surface of the grating medium in at least some spatial locations the grating structure comprising:
a first distribution of gratings disposed at a first location in the grating medium and having a first distribution of spatial frequencies and oriented in a first distribution of directions, and
a second distribution of gratings disposed at a second location in the grating medium and having a second distribution of spatial frequencies different than the first distribution of spatial frequencies and oriented in a second distribution of directions, the second distribution of directions being substantially the same as the first distribution of directions.
10. An optical reflecting device comprising:
a grating medium;
a grating structure occupying a volume within the grating medium, wherein:
the grating structure is structured to reflect incident light having a first wavelength and a first range of incidence angles about a substantially uniform first reflective axis, the incident light being incident upon a surface of the grating medium at a first location,
the grating structure is structured to reflect incident light having a second wavelength and a second range of incidence angles about a substantially uniform second reflective axis, the light being incident upon the surface of the grating medium at a second location, and
the substantially uniform first reflective axis differs from the substantially uniform second reflective axis by at least 0.1 degrees.
11. The optical reflecting device of claim 10 , wherein:
the first wavelength differs from the second wavelength by at least 50 nm; and
the first range of incidence angles is the same as the second range of incidence angles.
12. The optical reflecting device of claim 11 , wherein the first range of incidence angles is at least 15 degrees.