Patent ID: 7872788

Claim:
A method of digitally processing light waves passing through a planar structure having given functions f in (x, y, ω) and f out (x, y, ω) and consisting of a light-propagating and distributing layer, a plurality of interconnecting pattern elements of a holographic pattern in said of light-propagating and distributing layer, and a plurality of planar optical elements arranged in a predetermined pattern on the aforementioned light-propagating and distributing layer, the method comprising the steps of: calculating positions and shapes of the plurality of interconnecting pattern elements of a holographic pattern based on the aforementioned given functions f in (x, y, ω) and f out (x, y, ω) by a method of solving an inverse problem, said interconnecting pattern elements having refractive indices different from the refractive indices of the light-propagating and distributing layer, said method comprising the steps of: manufacturing the interconnecting pattern elements of the holographic pattern based on the results of the calculations; digitizing the aforementioned continuous functions f in ⁡ ( x , y , ω ) ≅ ∑ n , u ⁢ C n ⁢ ⁢ u ⁢ exp ⁡ ( ik n ⁢ r u ) ⁢ f ⁡ ( ω ) and f out ⁡ ( x , y , ω ) ≅ ∑ m , v ⁢ C m ⁢ ⁢ v ⁢ exp ⁡ ( - ik m ⁢ r v ) ⁢ f ⁡ ( ω ) by providing finite numbers (“n”, “m”, “u”, “v”) of values as a result of decomposition into the Fourier series; where k n , is the wave vector of an incoming wave, and r u is the distance from the incoming port number u to a current point; and k m , is the wave vector of an outgoing wave, and r v , is the distance from the outgoing port number v to a current point; and using the obtained digitized planar holographic pattern for converting the function f in (x, y, ω) into the function f out (x, y, ω).