Optical element, device, method, and applications

An optical imaging device, consisting of:

• an optical element characterized by a light transmission function, P(ξ, η), such that light within the spectrum of focusable radiation incident on the optical element from a point location in an object space of the optical element is optically transformed by P(ξ, η) into a band-limited uniformly redundant array (bl-URA), A(x,y), in an image space of the optical element;
• a detector disposed in the image space such that the bl-URA is formed on the detector;
• and
• an image processor adapted to recover an image of an object from the detected bl-URA.

A method for determining a transmission function P(ξ, η) for an optical element that will generate a desired intensity pattern A(x,y) on a detector from light within a spectrum of focusable radiation from a point on an object, comprising:

• a) determining a real, non-negative, band-limited uniformly redundant array, A(x,y), that will be generated on a detector by an optical element characterized by a transmission function P(ξ, η), from light within the spectrum of focusable radiation from a point on the object;
• b) defining an electric field having an amplitude E(x,y)=[A(x,y)]1/2;
• c) calculating the transmission function P(ξ, η) in a plane immediately adjacent a known position of the optical element by performing a free space back propagation, and denoting the transmission function |P(ξ, η)|exp[iφ(ξ,η)];
• d) determining an electric field at a known detector plane location by performing a free space propagation, and denoting this electric field F(x,y)exp[iψ(x,y)[;
• e) applying a detector plane intensity constraint by setting F(x,y)→[A(x,y)]1/2;
• f) performing another free space back propagation;
• and
• g) calculating the optical element transmission function P(ξ, η) that will generate the desired intensity pattern A(x,y).