Efficient, dynamic, high contrast lensing with applications to imaging, illumination and projection

Apparatus for controlling a phase modulator to display an image defined by image data, the apparatus comprising a data processor in communication with the phase modulator, the data processor configured to:

• determine an objective function based on the image data;
• transform the objective function into a frequency space;
• minimize the transformed objective function in the frequency space to obtain a phase function in the frequency space;
• and
• inverse transform the phase function to obtain a solution phase function relating the phase of the phase modulator to a position in two dimensions.

A method for controlling a phase modulator to display an image defined by image data, the method comprising:

• determining an objective function based on the image data;
• transforming the objective function into a frequency space;
• minimizing the transformed objective function in the frequency space to obtain a phase function in the frequency space;
• and
• inverse transform the phase function to obtain a solution phase function relating the phase of the phase modulator to a position in two dimensions.