Patent ID: 7440188

Claim:
A diffractive optical element (DOE) comprising: R×S lengthwise and crosswise aligning pixels {C mn } (m=1, 2, . . . , R; n=1, 2. . . , S) of a size of a×b which have g (=2 s : s: integer) different values of thicknesses {d mn } varying within one wavelength of laser light λ and have g (=2 s : s: integer) different values of complex amplitude transmittance {t mn } given by t mn =exp(j2π(n−1)d mn /λ), where j is an imaginary number unit and where n is a diffractive index of the DOE, complex amplitude W(α, β) of a beam diffracted in a direction of a horizontal angle α and a vertical angle β being calculated not by the Fast Fourier Transform but by, W ⁢ ⁢ ( α , β ) = sin ⁢ ⁢ c ⁢ ⁢ ( a ⁢ ⁢ α λ ) ⁢ ⁢ sin ⁢ ⁢ c ⁢ ⁢ ( b ⁢ ⁢ β λ ) ⁢ ⁢ ∑ m ⁢ ⁢ ∑ n ⁢ ⁢ t mn ⁢ exp ⁢ { - j ⁢ ⁢ k ⁢ ⁢ ( ma ⁢ ⁢ α + nb ⁢ ⁢ β ) } where summations are carried out for all the pixels in the DOE and some or all of the diffraction beam angles (α, β) are non-lattice points defined on an object plane, in the case of diverging an incident laser beam into K diffracted beams, the k-th beam having angles (α k , β k ) to an incident beam axis, the angles (α k , β k ) of the k-th diffracted beam (k=1, 2, . . . , K) satisfying equations, sin α k =m k U, sin β k =n k V, where m k and n k are integers having no common divisor and U and V are the positive greatest common divisors (measures) for {sin α k } and {sin β k } for k=1, 2, . . . , K, and both or either of the greatest common divisors U and V being smaller than a quotient λ/aR or λ/bS of the laser wavelength λ divided by a size aR or bS of the DOE, that is, U<λ/aR, V<λ/bS.