Patent ID: 8804244

Claim:
A method for manufacturing a diffraction grating, the method comprising: providing a substrate having a first surface and a second surface opposite to the first surface; providing a first predetermined function associated with arrangement of grooves of the first grating and a second predetermined function associated with arrangement of grooves of the second grating, wherein the first predetermined function is f 1 ⁡ ( x 1 ) = d 1 ⁢ tan ⁢ ⁢ θ π ⁡ [ sin ⁢ ⁢ 2 ⁢ π ⁢ ⁢ x 1 d 1 - 1 2 ⁢ sin ⁢ ⁢ 4 ⁢ π ⁢ ⁢ x 1 d 1 + 1 3 ⁢ sin ⁢ ⁢ 6 ⁢ π ⁢ ⁢ x 1 d 1 ] and the second predetermined function is f 2 ⁡ ( x 2 ) = d 2 ⁢ ⁢ tan ⁢ ⁢ θ π ⁡ [ sin ⁢ ⁢ 2 ⁢ π ⁢ ⁢ x 2 d 2 - 1 2 ⁢ sin ⁢ ⁢ 4 ⁢ π ⁢ ⁢ x 2 d 2 + 1 3 ⁢ sin ⁢ ⁢ 6 ⁢ π ⁢ ⁢ x 2 d 2 ] , where θ is a half of an angle of two coherent beams used to manufacture the first and second grating, d1 is a period of the first grating, d2 is a period of the second grating, x1 is a longitudinal coordinate which has an origin at the center of the first grating, and x2 is another longitudinal coordinate which has another origin at the center of the second grating; transforming the first function into a first Fourier series and the second function into a second Fourier series; forming the first grating on the first surface of the substrate using a fast tool servo system according to the first Fourier series; forming the second grating on the second surface using the fast tool servo system according to the second Fourier series.