Image phase retrieval

• US 9,939,781 B2
• Filed: 10/28/2016
• Issued: 04/10/2018
• Est. Priority Date: 04/12/2012
• Status: Active Grant

• Current Assignee: Dualitas Ltd. (Envisics, LLC)
• Original Assignee: Two Trees Photonics Limited (DAQRI, LLC)
• Inventors: Christmas, Jamieson
• Primary Examiner(s): Allen, Stephone B
• Assistant Examiner(s): DABBI, JYOTSNA V
• Application Number:
  US15/338,043
• Publication Number:
  US 20170045859A1
• Time in Patent Office: 529 Days
• Field of Search: 359 9
• CPC Class Codes: G02B 2027/0109 comprising details concerning the making of holograms
• CPC Class Codes: G02B 2027/014 comprising information/image processing systems
• CPC Class Codes: G02B 27/0101 characterised by optical features G02B27/0172 takes precedence
• CPC Class Codes: G02B 27/0103 comprising holographic elements
• CPC Class Codes: G03H 1/041 Optical element in the object space affecting the object beam, not otherwise provided for
• CPC Class Codes: G03H 1/0808 Methods of numerical synthesis, e.g. coherent ray tracing [CRT], diffraction specific
• CPC Class Codes: G03H 1/16 using Fourier transform G03H1/10, G03H1/12, G03H1/14 take precedence; analogue computers G06G, e.g. G06G7/19
• CPC Class Codes: G03H 1/2294 Addressing the hologram to an active spatial light modulator
• CPC Class Codes: G03H 2001/0816 Iterative algorithms
• CPC Class Codes: G03H 2210/20 2D object
• CPC Class Codes: G03H 2210/30 3D object
• CPC Class Codes: G06T 3/4053 based on super-resolution, i.e. the output image resolution being higher than the sensor resolution
• CPC Class Codes: G06T 3/4084 in the transform domain, e.g. fast Fourier transform [FFT] domain scaling

Abstract

A method of processing a pixellated image to retrieve a phase distribution representative of the image. The phase distribution representative of the image is in the Fourier domain. The method includes padding the image pixels with padding, or non-image, pixels to increase the total number of pixels in the pixellated image. The method further includes processing the padding or non-image pixels differently to the image pixels in each iteration of the iterative method.

Claims

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.