Discrete fractional fourier numerical environments for computer modeling of image propagation through a physical medium in restoration and other applications

• US 8,094,969 B2
• Filed: 02/28/2011
• Issued: 01/10/2012
• Est. Priority Date: 02/25/1999
• Status: Expired due to Fees

• Current Assignee: NRI R&D Patent Licensing, LLC (Advanced Touchscreen and Gesture Technologies, LLC)
• Original Assignee: Lester F. Ludwig
• Inventors: Ludwig, Lester F.
• Primary Examiner(s): PATEL, KANJIBHAI B
• Application Number:
  US13/037,342
• Publication Number:
  US 20110200272A1
• Time in Patent Office: 316 Days
• Field of Search: 382254-255, 382274-275, 382/280, 382/312, 359/29, 359/31, 359/279, 359/560, 709/232, 356/121
• US Class Current: 382/280
• CPC Class Codes: G02B 27/0012 Optical design, e.g. procedures, algorithms, optimisation routines
• CPC Class Codes: G02B 27/46 Systems using spatial filters
• CPC Class Codes: G06E 3/001 Analogue devices in which mathematical operations are carried out with the aid of optical or electro-optical elements optical elements per se G02B; devices consisting of a plurality of solid state components, including light sensitive semiconductor components, formed in or on a common substrate H01L27/14; electro-, magneto- or acousto-optics, non-linear optics G02F1/00; graph reading G06K11/00
• CPC Class Codes: G06T 2207/20056 Discrete and fast Fourier transform, [DFT, FFT]
• CPC Class Codes: G06T 2207/20201 Motion blur correction
• CPC Class Codes: G06T 5/10 using non-spatial domain filtering
• CPC Class Codes: G06T 5/73 Deblurring; Sharpening

Abstract

A system for numerically modeling evolution of an image propagating through a medium includes image using image data and a propagation medium model. The propagation medium model aligns a propagation centerline of the propagation medium model relative to the center of the image data. The propagation medium model has a numerical operator for applying an index-shifted numerical fractional Fourier transform operation on the image data, and aligning the zero original-domain origin relative to the center of the image data. The image data has spatially-indexed amplitude values and a center located relative to the spatially-indexed amplitude values. The propagation medium model has quadratic phase properties which are defined relative to a propagation centerline of the propagation medium model. Aligning the zero original-domain origin relative to the center of the image data to produces transformed image data having a zero frequency-domain origin that is centered within the transform-domain indices.

Claims

1. A method for numerically modeling evolution of an image propagating through a medium, the method comprising:

representing an image using image data comprising a plurality of spatially-indexed amplitude values, the image data comprising a center located relative to the plurality of spatially-indexed amplitude values;

providing a propagation medium model comprising quadratic phase properties which are defined relative to a propagation centerline of the propagation medium model;

aligning the propagation centerline of the propagation medium model relative to the center of the image data;

approximating the propagation medium model with a numerical operator for applying an index-shifted numerical fractional Fourier transform operation on the image data, the numerical operator having original-domain indices and transform-domain indices, wherein the original-domain indices comprise a zero original-domain origin that is centered within the original-domain indices, and the transform-domain indices comprise a zero transform-domain origin that is centered within the transform-domain indices; and

aligning the zero original-domain origin relative to the center of the image data to produce transformed image data comprising a zero frequency-domain origin that is centered within the transform-domain indices.

2. The method of claim 1, wherein the propagation medium model corresponds to effects induced by a single lens.

3. The method of claim 1, wherein the propagation medium model corresponds to effects induced by a system of lenses.

4. The method of claim 1, wherein the propagation medium model corresponds to effects induced by graded-index material.

5. The method of claim 4, wherein said graded-index material is an optical fiber.

6. The method of claim 1, wherein the image data comprises an image formed by light.

7. The method of claim 1, wherein the image data comprises an image formed by a particle beam.

8. The method of claim 1, wherein the transformed image data is structured to permit correction of misfocus in the image.

9. The method of claim 1, wherein the index-shifted numerical fractional Fourier transform operation further comprises a fractional power which is an adjustable parameter.

10. The method of claim 1, wherein the modeled medium comprises a spatial separation.

11. The method of claim 1, wherein the index-shifted numerical fractional Fourier transform operation is obtained by reorganizing operations on the eigenvectors for a traditional numerical discrete Fourier transform matrix or tensor.

12. The method of claim 1, wherein the center of the image data is either an exact center or an approximate center.