SEE THROUGH AXIAL HIGH ORDER PRISM
An optical arrangement for a head mounted display, having optical surface that can be described by standard mathematical equations. A prism element is used having three optical surfaces, and wherein the reference surface of the three optical surfaces are centered at, and have no tilt, relative to the optical axis. The prism has first surface that faces the display device and comprises a high order polynomial surface with a reference plane orthogonal to the optical axis. All of the surfaces of the prism are described by extended polynomials defined on a Cartesian coordinates having the z-axis coinciding with the optical axis.
1 . A prism for an optical apparatus, the optical apparatus having a viewing pupil and defining an optical axis through the viewing pupil, wherein the prism comprises:
three optical surfaces, wherein the surface form of the three optical surfaces are formed to have the origin centered at the optical axis when said prism is installed in the optical apparatus; and,
when said prism is installed in the optical apparatus, a first surface of the three optical surfaces faces a display device and comprises a high order extended polynomial surface with a reference plane orthogonal to the optical axis.
2 . The prism of claim 1 , wherein each of the three optical surfaces is formed as axial high order extended polynomials.
3 . The prism of claim 1 , wherein each of the high order extended polynomial is derived in Cartesian coordinates having a z-axis coinciding with the optical axis.
4 . The prism of claim 1 , wherein origin of the first surface is translated along the optical axis in the direction away from the viewing pupil.
5 . The prism of claim 4 , wherein origin of second surface of the three surfaces is at the intersection of the second surface and the optical axis, and the origin of the third surface of the three surfaces is at the intersection of the third surface and the optical axis.
6 . The prism of claim 1 , wherein a third surface of the three surfaces includes a full or partial mirror coating.
7 . The prism of claim 6 , wherein the three surfaces are symmetric along an YZ-plane, wherein Z-axis of the YZ-plane coincides with the optical axis and Y-axis of the YZ-plane is orthogonal to the optical axis.
8 . The prism of claim 3 , wherein each of the three optical surfaces is formed as axial high order extended polynomials extended at least to a fourth order term.
9 . The prism of claim 3 , wherein each of the three optical surfaces is formed as axial high order extended polynomials extended to from a fourth order term up to a twentieth order term in even increments.
10 . The prism of claim 3 , further comprising anti-reflection coatings on at least one of the first surface and second surface.
11 . An optical arrangement configured to be installed in an optical see-through head-mounted display defining an optical axis, comprising:
a prism having:
a first surface configured to receive light from a micro-display and configured to transmit the received light into the body of the prism;
a second surface configured to receive the light transmitted into the body of the prism from the first surface and configured to totally internally reflect the received light at the second surface; and
a third surface configured to receive the light reflected by the second surface and configured to reflect the light out of the prism towards a pupil of the head-mounted display;
wherein each of the first, second and third optical surfaces is formed as high order extended polynomial, having reference plane that is centered with respect to the optical axis, and has no tilt with respect to the optical axis.
12 . The optical arrangement of claim 11 , wherein origin of the first surface is translated along the optical axis in the direction away from a viewing pupil at a position external to the prism.
13 . The optical arrangement of claim 11 , wherein each of the first, second and third optical surfaces is symmetric along a YZ-plane, wherein Z-axis of the YZ plane coincides with the optical axis.
14 . The optical arrangement of claim 11 , wherein each of the first, second and third optical surfaces is formed as axial high order extended polynomials extended at least to a fourth order term.
15 . The optical arrangement of claim 11 , wherein each of the first, second and third optical surfaces is formed as axial high order extended polynomials extended at least to from a fourth order term to a twentieth order term in even increments.
16 . The optical arrangement of claim 11 , further comprising a corrector lens having a first surface shaped to mate with the third surface of the prism and a second surface facing away from the pupil.
17 . The optical arrangement of claim 16 , wherein the first and second surfaces of the corrector lens are defined by an axial high order polynomial surface with a reference plane orthogonal to the optical axis.
18 . The optical arrangement of claim 17 , further comprising anti-reflection coatings on at least one of the surfaces of the prism and the corrector lens.
19 . A method for forming optical elements for a head mounted display (HMD) comprising:
defining an optical axis as a straight line from a pupil of the HMD to an aperture of the HMD;
fabricating a prism by forming a first surface configured to face a micro-display installed in the HMD, the forming of the first surface is performed by defining the surface form of the first surface by a high order expanded polynomial having an origin centered on the optical axis and a z-axis coinciding with the optical axis; forming a second surface configured to face the pupil, the forming of the second surface is performed by defining the surface form of the second surface by a high order expanded polynomial having an origin centered on the optical axis and a z-axis coinciding with the optical axis; and forming a third surface configured to face the aperture, the forming of the third surface is performed by defining the surface form of the third surface by a high order expanded polynomial having an origin centered on the optical axis and a z-axis coinciding with the optical axis.
20 . The method of claim 19 , further comprising offsetting the origin of the first surface in a direction away from the pupil and at a position external to the prism along the optical axis.
21 . The method of claim 20 , further comprising forming a corrector lens, the corrector lens having a first surface configured to face the third surface of the prism and having a second surface configured to face the aperture, wherein the first and second surfaces of the corrector lens are formed by defining the surface form of the first and second surfaces by a high order expanded polynomial having an origin centered on the optical axis and a z-axis coinciding with the optical axis.