# US 2014/0193091 A1 · Correction of over-focus in digital images using centered discrete imaginary-power fractional fourier transformations with high-accuracy orthonormal eigenvectors

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- Number: US 2014/0193091 A1
- Document ID: US20140193091A1
- Status: Published application
- Kind: A1
- Application number: 14/207,186
- Filed: 2014-03-12
- Published: 2014-07-10
- Earliest claimed: 2009-11-15
- Inventors: Lester F. Ludwig
- Web page: https://patentgrep.com/patent/US20140193091A1

## CPC

- G06T 5/73: Deblurring; Sharpening
- G06T 5/10: using non-spatial domain filtering
- G06T 2207/20056: Discrete and fast Fourier transform, [DFT, FFT]
- G06T: IMAGE DATA PROCESSING OR GENERATION, IN GENERAL

## Abstract

A method for correcting overfocus of a digital image created from coherent imaging using centered fractional Fourier transforms or mathematical equivalents is described. A received image is presented to a numerical processor, and a first numerical value for an imaginary power variable is selected and used in an iterative algorithm, numerical procedure, system architecture, etc. A centered discrete fractional Fourier transform of an imaginary power and a phase restore operator associated are applied to the image file to produce a modified image. A change in mis-focused is determined and used in adjusting the specified imaginary power for a next iteration.

## Claims

### Claim 1

A method for correcting mis-focus of an image, the method comprising:
receiving an image file at a numerical processor, the image file comprising a portion of the image in an original mis-focused condition, the mis-focused condition comprising an over-focus condition for at least a portion of the image;
selecting a numerical value for a variable a;
beginning a first iteration of a numerical procedure executing on the numerical processor;
in the numerical procedure, applying a two-dimensional reflection operator composed with a two-dimensional centered discrete fractional Fourier transform operator of imaginary power i χ to the image file and applying a phase correction operator associated with the two-dimensional centered discrete fractional Fourier transform matrix of power 2−i χ to the image file, where is a real number and i is the square root of −1;
obtaining a modified portion of the image file from the above operations;
inspecting the modified portion of the image file and determining a change in the mis-focused condition;
based on the determined change, adjusting numerical value of x; and
beginning a next iteration of the numerical procedure on the numerical processor;
wherein a specific value of χ is chosen providing the best correction of the mis-focused condition.

### Claim 2 (depends on 1)

The method of claim 1, wherein the two-dimensional centered discrete fractional Fourier transform comprises two one-dimensional centered discrete fractional Fourier transform matrices, each such that the power of α=1 results in a centered discrete Fourier transform matrix and the power of α=2 results in a reflection matrix.

### Claim 3 (depends on 1)

The method of claim 1, wherein the reflection matrix reverses the sequence order of the elements of a vector on which the reflection matrix operates.

### Claim 4 (depends on 1)

The method of claim 1, wherein the two-dimensional centered discrete fractional Fourier transform operator of power i χ is applied after applying the phase correction operator associated with a two-dimensional centered discrete fractional Fourier transform matrix of power 2−iχ.

### Claim 5 (depends on 1)

The method of claim 1, wherein the two-dimensional centered discrete fractional Fourier transform operator of power iχ is applied before applying the phase correction operator associated with a two-dimensional centered discrete fractional Fourier transform matrix of power 2−iχ.

### Claim 6 (depends on 1)

The method of claim 1, wherein number χ is a positive number.

### Claim 7 (depends on 1)

The method of claim 1, wherein number χ is a negative number.

### Claim 8 (depends on 1)

The method of claim 1, wherein the image is an image created by coherent imaging.

### Claim 9 (depends on 1)

The method of claim 1, wherein the image is an image created by electron imaging.

### Claim 10 (depends on 1)

The method of claim 1, wherein the image is an image created by light imaging.

### Claim 11 (depends on 1)

The method of claim 1, wherein the two-dimensional centered discrete fractional Fourier transform operator is represented as a 4-dimensional array.

### Claim 12 (depends on 1)

The method of claim 1, wherein the two-dimensional centered discrete fractional Fourier transform operator is represented as a 4-dimensional tensor.

### Claim 13 (depends on 1)

The method of claim 1, wherein the two-dimensional centered discrete fractional Fourier transform operator is applied as a first one-dimensional centered discrete fractional Fourier transform matrix operating on columns of the image file and a second one-dimensional centered discrete fractional Fourier transform matrix operating on rows of the image file.

### Claim 14 (depends on 1)

The method of claim 1, wherein the phase correction operator is a 4-dimensional tensor.

### Claim 15 (depends on 1)

The method of claim 1, wherein the phase correction operator is a 4-dimensional array.

### Claim 16 (depends on 1)

The method of claim 1, wherein the phase correction is applied as a first one-dimensional phase correction operator matrix on columns of the at least portions of the image file and a second one-dimensional phase correction operator matrix operating on rows of the at least portions of the image file.

### Claim 17 (depends on 1)

The method of claim 1 wherein the modified portion of the image file comprising the best correction of the mis-focused condition is provided as an output.