Image phase retrieval

1. An iterative method of processing a pixellated image comprising image pixels to retrieve a phase distribution representative of the image in the Fourier domain, the method comprising:

padding the image pixels with non-image pixels to increase the total number of pixels in the pixellated image, wherein the values of the non-image pixels comprises an initial random noise field;

associating each pixel of the pixellated image with a phase value to form a first data set having plural elements, each element of the first data set having amplitude information and phase information; and

(n+1) iterations of the following steps, where n is an integer:

performing a Fourier transform of the first data set to produce a second data set having plural elements, each element of the second data set having amplitude and phase information;

quantizing the phase information from the second data set;

forming a third data set having plural elements, each element of the third data set having amplitude and phase information, the phase information being derived from the second data set and;

inverse Fourier transforming the third data set to produce a fourth data set having plural elements, each element of the fourth data set having amplitude and phase information;

overwriting the amplitude and/or phase information of the fourth data set to produce a fifth data set having plural elements, each element of the fifth data set having amplitude and phase information;

wherein overwriting comprises processing the nonimage pixels differently to the image pixels and attenuating the amplitude information of each non-image pixel of the fifth data set by an attenuation factor and/or processing the amplitude information of the each image pixel utilizing a gain factor;

wherein the attenuation factor and/or gain factor are variable and dependent on the iteration number of the iterative method; and

using the modified fifth data set as the first data set of the next iteration; and

reconstructing the phase distribution to form a holographic reconstruction of the image.

2. A method as claimed in claim 1 wherein the non-image pixels are processed by replacing the value of at least some of the non-image pixels.

3. A method as claimed in claim 1 wherein at least some of the non-image pixels comprises those non-image pixels having a value above a predetermined threshold.

4. A method as claimed in claim 1 wherein at least some of the non-image pixels comprises all non-image pixels.

5. A method as claimed in claim 1 wherein at least some of the non-image pixels are replaced by a predetermined value.

6. A method as claimed in claim 2 wherein the non-image pixels are replaced by a random noise field.

7. A method as claimed in claim 1 wherein the random noise field is an initial random noise field for the first iteration.

8. A method as claimed in claim 1 wherein the non-image pixels form a border around the image pixels.

9. A method as claimed in claim 1 wherein the image is the nth frame of a 2D sequence of video frames.

10. A projection system comprising:

a processor arranged to perform the method of claim 1 ;

a spatial light modulator arranged to display the phase distribution;

a light source arranged to illuminate the spatial light modulator; and

a Fourier transform lens arranged to perform an optical frequency-space transformation on the light output from the spatial light modulator.

11. A head-up display comprising the projector as claimed in claim 10 .

12. A projection system comprising:

a processor arranged to:

receive a pixellated image comprising image pixels;

padding the image pixels with non-image pixels to increase the total number of pixels in the pixellated image, wherein the values of the non-image pixels comprise an initial random noise field;

associate each pixel of the pixellated image with a phase value to form a first data set having plural elements, each element of the first data set having amplitude information and phase information; and

(n+1) iterations of the following steps, where n is an integer:

perform a Fourier transform of the first data set to produce a second data set having plural elements, each element of the second data set having amplitude and phase information;

quantize the phase information from the second data set;

form a third data set having plural elements, each element of the third data set having amplitude and phase information, the phase information being derived from the second data set and;

inverse Fourier transform the third data set to produce a fourth data set having plural elements, each element of the fourth data set having amplitude and phase information;

overwrite the amplitude and/or phase information of the fourth data set to produce a fifth data set having plural elements, each element of the fifth data set having amplitude and phase information; wherein overwriting comprises processing the non-image pixels differently to the image pixels and attenuating the amplitude information of each non-image pixel of the fifth data set by an attenuation factor and/or processing the amplitude information of the each image pixel utilizing a gain factor; wherein the attenuation factor and/or gain factor are variable and dependent on an iteration number; and

use the modified fifth data set as the first data set of a next iteration;

a spatial light modulator arranged to display a phase distribution;

a light source arranged to illuminate the spatial light modulator; and

a Fourier transform lens arranged to perform an optical frequency-space transformation on the light output from the spatial light modulator to form a holographic reconstruction of the image.