Optical device with a pair of diffractive optical elements

1. Optical device comprising a pair of plate-like diffractive optical elements (DOEs) with transmission functions T 1 (r,θ)=exp[iΦ 1 (r,θ)] and T 2 (r, θ)=exp[iΦ 2 (r,θ)] where r and θ are polar coordinates, r being the radius and θ being the polar angle, and Φ 1,2 (r,θ) are phase profiles within 0 and 2π imprinted on the DOEs, the two DOEs being successively arranged in parallel to each other with a sufficiently small separation between them that the combination of the two adjacent DOEs corresponds optically to one single DOE with a transmission function of T combi =T 1 *T 2 , one (or both) of the DOEs being adapted to be rotated relative to the other around an axis perpendicular to the surface, so that the pair of DOEs acts as a DOE with the transmission function

T combi = T 1 ( r ,θ)* T 2 ( r ,θ−φ)=exp[ iΦ 1 ( r ,θ)]*exp[ iΦ 2 ( r ,θ−φ)]==exp[i{Φ 1 ( r,θ)+Φ 2 (r,θ−φ)}] where φ is the relative angle of rotation,

wherein the phase profiles Φ 1,2 of the two DOEs are given by

Φ 1 ( r ,θ)=mod 2π {[ F ( r )θ+ m phas θ+ a spir θ 2 ]+[ G offs ( r )/2]+ a div r 2 } and

Φ 2 ( r ,θ)=mod 2π {−[ F ( r )θ+ m phas θ+ a spir θ 2 ]+[ G offs ( r )/2]− a div r 2 },

where mod 2π {. . . } means the modulo 2π operation, where m phas is an integer number or zero, where the coefficients a spir and a div are real numbers or zero and where F(r) and G offs (r) are real functions depending on r but not on θ, F(r) and G(r) chosen so that each of the corresponding transfer functions T F (r)=exp[iF(r)] and T G (r)=exp[iG offs (r)] respectively is the transfer function of either a (rotationally symmetrical) Lens or of a (rotationally symmetrical) axicon or of an arbitrary superposition thereof, wherein G offs (r) may also be zero for all values of r and wherein F(r) may also be zero for all values of r, yet under the condition that in this case (i.e. F(r)=0) at least one of the coefficients m phas or a spir , is not zero.

2. Optical device according to claim 1 , wherein the phase profiles Φ 1,2 of the two DOEs are given by

Φ 1 ( r ,θ)=mod 2π {[ a lens r 2 θ+ a axic rθ+m phas θ+ a spir θ 2 ]+( a offs /2) r 2 + a div r 2 } and

φ 2 ( r ,θ)=mod 2π {[ a lens r 2 θ+ a axic rθ+m phas θ+ a spir θ 2 ]+( a offs /2) r 2 − a div r 2 },

where mod 2π {. . . } means the modulo 2π operation and where the coefficients a lens , a axic , a spir , a offs and a div are real numbers which also may be zero and the coefficient m phas is an integer number or zero, yet where at least one of the coefficients a lens , a axic , m phas or a spir is not zero.

3. Optical device according to claim 1 , wherein the maximum relative rotation of the two DOEs is limited by the extremal rotation angles φ min and φ max which fulfill the condition [−90°≦φ min <φ<φ max ≦+90], where φ is the relative rotation angle.

4. Optical device according to claim 1 , further comprising a sector-shaped light-absorber which at least covers an angular sector of the pair of DOEs, wherein said covered angular has an angular aperture of α cov =φ max −φ min .

5. Optical device according to claim 1 , further comprising a light-absorber with variable geometry, wherein this light-absorber is adapted to cover an angular sector of the pair of DOEs, said covered sector having the angular aperture of φ, where φ is the actual relative rotation angle.

6. Optical device comprising a pair of plate-like diffractive optical elements (DOEs) with transmission functions T 1 (r,θ)=exp[iΦ 1 (r,θ)] and T 2 (r,θ)=exp[iΦ 2 (r,θ)] where r and θ are polar coordinates, r being the radius and θ being the polar angle, and Φ 1,2 (r,θ) are phase profiles within 0 and 2π imprinted on the DOEs, the two DOEs being successively arranged in parallel to each other with a sufficiently small separation between them that the combination of the two adjacent DOEs corresponds optically to one single DOE with a transmission function of T combi =T 1 *T 2 , one (or both) of the DOEs being adapted to be rotated relative to the other around an axis perpendicular to the surface, so that the pair of DOEs acts as a DOE with the transmission function

T combi = T 1 ( r ,θ)* T 2 ( r ,θ−φ)=exp[ iΦ 1 ( r ,θ)]*exp[ iΦ 2 ( r ,θ−φ)]==exp[ i{Φ 1 (r,θ)+Φ 2 (r,θ−φ)}] where φ is the relative angle of rotation,

wherein the phase profiles Φ 1,2 of the two DOEs are given by

φ 1 ( r ,θ)=mod 2π {[round{ F ( r )}θ+ m phas θ]+[ G offs ( r )/2]+ a div r 2 } and

φ 2 ( r ,θ)=mod 2π {−[round{ F ( r )}θ+ m phas θ]+[ G offs ( r )/2]− a div r 2 },

where mod 2π {. . . } means the modulo 2π operation, where m phas is an integer number or zero, where the coefficient a div , is a real number or zero and where F(r) and G offs (r) are real functions depending on r but not on θ, F(r) and G(r) chosen so that each of the corresponding transfer functions T F (r)=exp[iF(r)] and T G (r)=exp[iG offs (r)] respectively is the transfer function of either a (rotationally symmetrical) Lens or of a (rotationally symmetrical) axicon or of an arbitrary superposition thereof, wherein G offs (r) may also be zero for all values of r and wherein F(r) may also be zero for all values of r, yet under the condition that in this case [i.e. F(r)=0] the coefficient m phas is not zero.

7. Optical device according to claim 6 , wherein the phase profiles Φ 1,2 of the two DOEs are given by

φ 1 ( r ,θ)=mod 2π {[round{ a lens r 2 +a axic r}θ+m phas θ]+( a offs /2) r 2 +a div r 2 } and

φ 2 ( r ,θ)=mod 2π {−[round{ a lens r 2 +a axic r}θ+m phas θ]+( a offs /2) r 2 −a div r 2 },

where mod 2π {. . . } means the modulo 2π operation, round {. . . } means rounding of the argument to the next higher integer number and where a lens , a axic , a offs and a div are freely selectable coefficients which also may be zero and the coefficient m phas is an integer number or zero, yet where at least one of the coefficients a lens , a axic or m phas is not zero.

8. Optical device according to claim 1 , wherein one of the diffractive optical elements is adapted to continuously rotate with an angular frequency ω rot for continuously changing those optical properties of the optical device that depend on the rotation angle φ.

9. Optical device according to claim 6 , wherein one of the diffractive optical elements is adapted to continuously rotate with an angular frequency ω rot for continuously changing those optical properties of the optical device that depend on the rotation angle φ.

10. Optical device according to claim 1 , wherein the phase profile imprinted on the diffractive optical elements has pixels with a size of 10 μm or less.

11. Optical device according to claim 1 , wherein the phase profile imprinted on the diffractive optical elements has pixels with a size on the order of the light wavelength, or larger.

12. Optical device according to claim 6 , wherein the phase profile imprinted on the diffractive optical elements has pixels with a size of 10 μm or less.

13. Optical device according to claim 6 , wherein the phase profile imprinted on the diffractive optical elements has pixels with a size on the order of the light wavelength, or larger.