# US 8,542,945 B1 · Correction of mis-focus in recorded images using centered discrete fractional fourier transformations with high-accuracy orthonormal eigenvectors > Agents: this data is available as JSON from the patentgrep API and MCP server — see https://patentgrep.com/llms.txt - Number: US 8,542,945 B1 - Document ID: US8542945B1 - Status: Granted - Kind: B1 - Application number: 12/945,902 - Filed: 2010-11-15 - Granted: 2013-09-24 - Earliest claimed: 2009-11-15 - Assignees: Lester F. Ludwig - Applicants: Lester F. Ludwig - Inventors: Lester F. Ludwig - Web page: https://patentgrep.com/patent/US8542945B1 ## 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 mis-focus of an 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 a variable α is selected and used in an iterative algorithm, numerical procedure, system architecture, etc. A centered discrete fractional Fourier transform of power α and a phase restore operator associated with a centered discrete fractional Fourier transform of power α are applied to the image file to produce a modified image. A change in mis-focused is determined and used in adjusting α for a next iteration. If values for α between 0 and real number β do not result in a desired outcome, α is adjusted as a complex value β+iχ where χ is a real number. ## 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; selecting a numerical value for a variable α; beginning a first iteration of a numerical procedure executing on the numerical processor; in the numerical procedure, applying a two-dimensional centered discrete fractional Fourier transform operator of power α to the image file and applying a phase correction operator associated with the two-dimensional centered discrete fractional Fourier transform matrix of power β−α to the image file; 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 α; and beginning a next iteration of the numerical procedure on the numerical processor; wherein if numerical values for the variable α between the real values of 0 and β do not result in a desired outcome, the numerical value for the variable α is adjusted to an imaginary value of the form iχ where χ is the imaginary part of α. ### Claim 2 (depends on 1) The method of claim 1, wherein the number β is real. ### Claim 3 (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=η results in a centered discrete Fourier transform matrix and the power of α=β results in a reflection matrix. ### Claim 4 (depends on 3) The method of claim 3, wherein the number η is real, and the reflection matrix reverses the sequence order of the elements of a vector on which the reflection matrix operates. ### Claim 5 (depends on 4) The method of claim 4, wherein number η is 0. ### Claim 6 (depends on 1) The method of claim 1, wherein the two-dimensional centered discrete fractional Fourier transform operator of power α is applied after applying the phase correction operator associated with a two-dimensional centered discrete fractional Fourier transform matrix of power β−α. ### Claim 7 (depends on 1) The method of claim 1, wherein the two-dimensional centered discrete fractional Fourier transform operator of power α is applied before applying the phase correction operator associated with a two-dimensional centered discrete fractional Fourier transform matrix of power β−α. ### Claim 8 (depends on 1) The method of claim 1, wherein number β is 2. ### Claim 9 (depends on 1) The method of claim 1, wherein number χ is a positive number. ### Claim 10 (depends on 1) The method of claim 1, wherein number χ is a negative number. ### Claim 11 (depends on 1) The method of claim 1, wherein the image is an image created by coherent imaging. ### Claim 12 (depends on 1) The method of claim 1, wherein the image is an image created by electron imaging. ### Claim 13 (depends on 1) The method of claim 1, wherein the image is an image created by light imaging. ### Claim 14 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; selecting a numerical value for a variable α; beginning a first iteration of a numerical procedure executing on the numerical processor; in the numerical procedure, applying a two-dimensional centered discrete fractional Fourier transform operator of power α to the image file and applying a phase correction operator associated with the two-dimensional centered discrete fractional Fourier transform matrix of power β−α to the image file; 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 α; and beginning a next iteration of the numerical procedure on the numerical processor; wherein if numerical values for the variable α between the real values of 0 and β do not result in a desired outcome, the numerical value for the variable α is adjusted to an imaginary value of the form iχ where χ is the imaginary part of α, wherein the two-dimensional centered discrete fractional Fourier transform operator is represented as a 4-dimensional array. ### Claim 15 (depends on 14) The method of claim 14, wherein the two-dimensional centered discrete fractional Fourier transform operator is represented as a 4-dimensional tensor. ### Claim 16 (depends on 14) The method of claim 14, 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 17 (depends on 14) The method of claim 14, wherein the phase correction operator is a 4-dimensional tensor. ### Claim 18 (depends on 14) The method of claim 14, wherein the phase correction operator is a 4-dimensional array. ### Claim 19 (depends on 14) The method of claim 14, wherein the phase correction is applied as a first one-dimensional phase correction operator matrix associated with a two-dimensional centered discrete fractional Fourier transform matrix of power β−α operating on columns of the at least portions of the image file and a second one-dimensional phase correction operator matrix associated with a two-dimensional centered discrete fractional Fourier transform matrix of power β−α operating on rows of the at least portions of the image file. ### Claim 20 A method for correcting a mis-focus of image file created from coherent imaging using centered fractional Fourier transforms or mathematical equivalents, the method comprising: receiving the mis-focused image at a numerical processor; selecting a first numerical value for a variable α iterating a numerical procedure using the variable α; in the numerical procedure, applying a centered discrete fractional Fourier transform of power α and a phase restore operator associated with a centered discrete fractional Fourier transform of power β−α to the image file to produce a modified image; and determining a change in the mis-focused image and using the change in the mis-focused image in adjusting α for a next iteration, wherein if values for α between 0 and real number β do not result in a desired outcome, α is adjusted to an imaginary value of the form iχ where χ is the imaginary part of α.