Apochromatic pancharatnam berry phase (PBP) liquid crystal structures for head-mounted displays
A Pancharatnam Berry Phase (PBP) liquid crystal structure for adjusting or focusing light of a plurality of color channels emitted by a display of a head-mounted display (HMD) comprises a plurality of PBP active elements. Each PBP active element of the structure is configured to act as a half waveplate for light of a corresponding color channel, such that light of the corresponding color channel is adjusted by a predetermined amount. In addition, each PBP active element acts as a one waveplate for light of the remaining color channels, such that light of the remaining color channels passes through the PBP active element substantially unaffected. As such, the PBP structure is able to adjust incident light of the plurality of color channels uniformly in an apochromatic fashion.
1. A Pancharatnam Berry Phase (PBP) liquid crystal structure comprising:
a first PBP active element configured to act as half waveplate for light of a first wavelength range corresponding to a first color channel of a set of color channels, such that light of the first wavelength range is adjusted by a first amount, and to act as a one waveplate for at least light of a second wavelength range corresponding to a second color channel of the set of color channels, such that light of the second wavelength range is able to pass through the first PBP active element without substantially changing direction; and
a second PBP active element configured to act as a half waveplate for light of the second wavelength range, such that light of the second wavelength range is adjusted by the first amount, and to act as a one waveplate for a least light of the first wavelength range, such that light of the first wavelength range is able to pass through the second PBP active element without substantially changing direction.
2. The PBP liquid crystal structure of claim 1 , wherein the first PBP active element is a first PBP liquid crystal grating that is configured to adjust light of the first wavelength range to a first angle, and the second PBP active element is a second PBP liquid crystal grating that is configured to adjust light of the second wavelength range to the first angle.
3. The PBP liquid crystal structure of claim 2 , wherein the first PBP liquid crystal grating has a first pitch, and the second PBP liquid crystal grating has a second pitch that is different than the first pitch.
4. The PBP liquid crystal structure of claim 3 , wherein the first pitch is directly proportional to a wavelength within the first range of wavelengths, and inversely proportional to a sine of the first angle.
5. The PBP liquid crystal structure of claim 4 , wherein the second pitch is directly proportional to a wavelength within the second range of wavelengths, and inversely proportional to a sine of the first angle.
6. The PBP liquid crystal structure of claim 1 , wherein the first PBP active element is a first PBP liquid crystal lens that is configured to focus light of the first wavelength range to a first location, and the second PBP active element is a second PBP liquid crystal lens that is configured to focus light of the second wavelength range to the first location.
7. The PBP liquid crystal structure of claim 6 , wherein the first PBP liquid crystal lens has a first liquid crystal rotation speed, and the second PBP liquid crystal lens has a second liquid crystal rotation speed that is different than the first liquid crystal rotation speed.
8. The PBP liquid crystal structure of claim 6 , wherein the first liquid crystal rotation speed is directly proportional to a first radial distance of the first PBP liquid crystal lens, and inversely proportional to a distance to the first location and a wavelength in the first range of wavelengths.
9. The PBP liquid crystal structure of claim 8 , wherein the second liquid crystal rotation speed is directly proportional to a second radial distance of the second PBP liquid crystal lens, and inversely proportional to a distance to the first location and a wavelength in the second range of wavelengths.
10. The PBP liquid crystal structure of claim 1 , wherein the first PBP active element and the second PBP active element are stacked to form a stacked structure, the stacked structure configured to receive a light comprising at least light of the first wavelength range and light of the second wavelength range, the light passing through the second active element prior to passing through the first active element.
11. The PBP liquid crystal structure of claim 1 , wherein the first PBP active element and the second PBP active element are part of an optical assembly of a head-mounted display (HMD).
12. The PBP liquid crystal structure of claim 1 , wherein the first range of wavelengths is a portion of a visible band of light comprising wavelengths between 390 nm and 700 nm, and the second range of wavelengths is a different portion of the visible band of light.
13. A head-mounted display (HMD), comprising:
an electronic display configured to emit image light that is inclusive of a set of color channels;
an optical assembly configured to optically correct for chromatic aberration for the set of color channels using a Pancharatnam Berry Phase (PBP) liquid crystal structure that outputs image light corrected for chromatic aberration for the set of color channels in accordance with color correction instructions, the PBP liquid crystal structure comprising:
a first PBP active element configured to act as half waveplate for light of a first wavelength range corresponding to a first color channel of the set of color channels, such that light of the first wavelength range is adjusted by a first amount, and to act as a one waveplate for at least light of a second wavelength range corresponding to a second color channel of the set of color channels, such that light of the second wavelength range is able to pass through the first PBP active element without substantially changing direction; and
a second PBP active element configured to act as a half waveplate for light of the second wavelength range, such that light of the second wavelength range is adjusted by the first amount, and to act as a one waveplate for a least light of the first wavelength range, such that light of the first wavelength range is able to pass through the second PBP active element without substantially changing direction.
14. The HMD of claim 13 , wherein the first PBP active element is a first PBP liquid crystal grating that is configured to adjust light of the first wavelength range to a first angle, and the second PBP active element is a second PBP liquid crystal grating that is configured to adjust light of the second wavelength range to the first angle.
15. The HMD of claim 14 , wherein the first PBP liquid crystal grating has a first pitch, and the second PBP liquid crystal grating has a second pitch that is different than the first pitch.
16. The HMD of claim 15 , wherein the first pitch is directly proportional to a wavelength within the first range of wavelengths, and inversely proportional to a sine of the first angle.
17. The HMD of claim 13 , wherein the first PBP active element is a first PBP liquid crystal lens that is configured to focus light of the first wavelength range to a first location, and the second PBP active element is a second PBP liquid crystal lens that is configured to focus light of the second wavelength range to the first location.
18. The HMD of claim 17 , wherein the first PBP liquid crystal lens has a first liquid crystal rotation speed, and the second PBP liquid crystal lens has a second liquid crystal rotation speed that is different than the first liquid crystal rotation speed.
19. The HMD of claim 18 , wherein the first liquid crystal rotation speed is directly proportional to a first radial distance of the first PBP liquid crystal lens, and inversely proportional to a distance to the first location and a wavelength in the first range of wavelengths.
20. The HMD of claim 13 , wherein the first range of wavelengths is a portion of a visible band of light, and the second range of wavelengths is a different portion of the visible band of light.