Efficient, dynamic, high contrast lensing with applications to imaging, illumination and projection
A new projector design combines one spatial light modulator that affects only the phase of the illumination, and one spatial light modulator that only affects its amplitude (intensity). The phase-only modulator curves the wavefront of light and acts as a pre-modulator for a conventional amplitude modulator. This approach works with both white light and laser illumination, generating a coarse image representation efficiently, thus enabling, within a single image frame, significantly elevated highlights as well as darker black levels while reducing the overall light source power requirements.
1 . 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.
2 . Apparatus according to claim 1 wherein the data processor being configured to transform the objective function comprises the data processor being configured to compute a Fourier transform of the objective function.
3 . Apparatus according to claim 2 wherein the data processor is configured to, before transforming, extend the image data to have periodic boundary conditions and base the objective function on the extended image data.
4 . Apparatus according to claim 3 wherein the data processor being configured to extend the image data comprises the data processor being configured to make a mirror image of the image data across each boundary of the image data.
5 . Apparatus according to claim 1 wherein the objective function is a least squares objective function.
6 . Apparatus according to claim 1 wherein the objective function includes a cost for deviating from an input argument.
7 . Apparatus according to claim 1 wherein the data processor is configured to iteratively determine the objective function, transform the objective function, and evaluate the transformed objective function, and in each of a plurality of iterations the input argument for the objective function is the solution phase function for a previous iteration.
8 . Apparatus according to claim 7 wherein the data processor is configured to cache a Fourier transform of the solution phase function for the previous iteration and apply the cached Fourier transform of the solution phase function in a current iteration.
9 . Apparatus according to claim 1 wherein the objective function comprises a proximal operator given by:
prox γF ( q )=(γ+ A T A ) −1 (γ q+A T b ).
10 . Apparatus according to claim 9 wherein the data processor being configured to evaluate the transformed objective function comprises the data processor being configured to determine
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11 . Apparatus according to claim 10 wherein one or more of:
A={circumflex over (f)}∇ 2 ;
b=1−I p k (v); and
α>0 is a regularization parameter.
12 . Apparatus according to claim 1 wherein the data processor is configured to initialize the phase surface as a constant value.
13 . Apparatus according to claim 1 wherein the data processor is configured to evaluate the transformed objective function in parallel for different points.
14 . Apparatus according to claim 13 wherein the data processor comprises a graphics processing unit and the graphics processing unit evaluates the transformed objective function.
15 . Apparatus according to claim 1 comprising the phase modulator and a light source for projecting light on the phase modulator, the data processor configured to control the phase modulator to display the image by controlling pixels of the phase modulator according to the solution phase function while controlling the light source to illuminate the phase modulator.
16 . Apparatus according to claim 15 wherein the light source is configured to evenly illuminate the phase modulator with collimated light.
17 . Apparatus according to claim 15 wherein the phase modulator comprises an array of liquid crystal pixels and the data processor is configured to set control signals to the pixels according to the solution phase function.
18 . Apparatus according to claim 17 wherein the phase modulator is one of: a LCoS phase modulator; and a deformable mirror.
19 . Apparatus according to claim 15 wherein at least one of: a maximum numerical aperture for points on the phase modulator is 0.21 or less and the phase modulator has a maximum phase retardation and apparatus comprises subtracting a multiple of 2π from phase shifts of the phase function that exceed the maximum phase retardation of the phase modulator.
20 . 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.