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; then

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 then

(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, the overwriting comprising processing the non-image pixels differently to the image pixels; the overwriting comprising replacing the value of the amplitude information of each non-image pixel of the fifth data set by a random noise field and/or processing the amplitude information of the each image pixel utilizing a gain factor, the gain factor being 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 random noise field is an initial random noise field for the first iteration.

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

4. The method according to claim 3 , wherein the ratio between the target image width and the border width is in the range of 75-90%.

5. The method according to claim 4 , wherein the gain factor used in the algorithm is in the range of 0.5 to 0.9.

6. The method according to claim 3 , wherein the gain factor used in the algorithm is in the range of 0.5 to 0.9.

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

8. The method according to claim 1 , wherein in each iteration, the overwriting comprises replacing the value of the amplitude information of each non-image pixel of the fifth data set by a random noise field.

9. The method according to claim 8 , wherein in each iteration, the overwriting comprises processing the amplitude information of the each image pixel utilizing a gain factor.

10. The method according to claim 1 , wherein in each iteration, the overwriting comprises processing the amplitude information of the each image pixel utilizing a gain factor.

11. A projection system comprising:

a processor arranged to perform 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; then

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 then

(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, the overwriting comprising processing the non-image pixels differently to the image pixels; the overwriting comprising replacing the value of the amplitude information of each non-image pixel of the fifth data set by a random noise field and/or processing the amplitude information of the each image pixel utilizing a gain factor, the gain factor being 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;

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.

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