AR optical element, method for manufacturing the same, and AR display device

A method for manufacturing an AR optical element wherein

• the AR optical element is configured to reflect or transmit a group of light rays incident from one or more projection devices and emit output light with a uniform intensity distribution over a predetermined angular width, and
• to have periodic structures of refractive index multiplexed with a predetermined interval and multiplicity, the periodic structures of the refractive index each has an optical normal in a different direction from a physical normal orthogonal to a plane of a micro-region that reflects or transmits the group of light rays, and
• wherein
• when an incident vector θIN denotes a direction of the group of light rays incident from the projection device;
• an output vector θOUT denotes a direction to a center position of an observation area;
• the predetermined angular width is denoted by ΦX and ΦY that are angular widths respectively in horizontal and vertical directions of the group of light rays reflected from or transmitted through the AR optical element;
• and angular intervals ΔθX and ΔθY, into which the angular widths ϕX and ϕY are respectively divided, denote spread angles respectively in the horizontal and vertical directions of the group of light rays incident from the projection device,
• a normal θnormal of the periodic structure of the refractive index is expressed by an equation (1) below
• [Math. 1]
• θnormal=(θIN+θOUT)/2−90° (1)
• an interval V of the periodic structure of the refractive index is expressed by an equation (2) below that includes a recording and reproducing wavelength λ of the AR optical element and an average refractive index no of the AR optical element
• [Math. 2]
• V=(λ/nO)|2 sin(θIN−θOUT)/2| (2);
• a multiplicity K of the periodic structure of the refractive index) in horizontal directions is expressed by an equation (3) below, wherein a floor(x) is a function that returns a maximum integer value less than or equal to x
• [Math. 3]
• K=floor(ϕX/ΔθX)+1 (3)
• a multiplicity L of the periodic structure of the refractive index in vertical directions is expressed by an equation (4) below
• [Math. 4]
• L=floor(ϕY/ΔθY)+1 (4);
• and
• a multiplicity M of the periodic structure of the refractive index in the horizontal and vertical directions is expressed by the following equation (5)
• [Math. 5]
• M=KL (5) and
• wherein
• the method includes steps of:
• calculating a normal θnormal, an interval V, and multiplicities K, L, and M;
• computing a computer-generated hologram so that the periodic structures of the refractive index having the normal θnormal are multiplexed with the interval V and the multiplicity M;
• and
• producing the AR optical element using a hologram printer based on a result of the computing of the computer-generated hologram.