Focus Correction


New Renaissance Institute’s founder is credited as the first to discover and report the fractional Fourier transform properties of lenses in the benchmark text The Fractional Fourier Transform with Applications in Optics and Signal Processing (p.386) some five years prior to the independent engulfing rise of the topic to widespread attention beginning in 1993. The recognized paper was accepted for presentation only as poster session at the 1985 SPIE Spatial Light Modulator Conference. Many hundreds of papers, including dozens that have since become celebrated, have been subsequently published beginning in 1993, and the work of two leading individuals in the 2003-initiated Fractional Fourier Transform publication “wave” were awarded the 1998 Prize of the International Commission for Optics.

New Renaissance Institute has continued its work in fractional Fourier transforms in the contexts of formal mathematical operator theory, fractional Hilbert-space operators, the theory of Special Functions, computational imaging, electron microscopy, coherent optics, visible-light imaging, and monolithic optical computing engines.

The items below pertain to NRI’s work in the area of light-field imaging and computational image refocusing involving phase-reconstruction for computational refocusing of legacy coherent images leveraging operator group and operator algebra properties of the fractional Fourier transform operator, for example for use in refocusing of legacy and real-time high-energy electron microscopy images but with many other potential optical applications. Mathematical aspects of this work include several aspects of the discrete fractional Fourier transform operator both in structure for proper approximate propagation modeling as well as numeric computation as well as complex-valued powers of the fractional Fourier transform operator.

NRI’s founder and NRI have performed other innovative work in light-field imaging and computational imaging, including its lensless imaging camera work

NRI is pleased to have hosted summer interns from U.C. Santa Cruz and U.C. Irvine who provided laboratory work for us in this technology area.

Issued Patents

TitlePatent NumberApplication NumberPriority DatesPDFText OnlyRelated Patents
Correction of over-focus in digital images using centered discrete imaginary-power fractional fourier transformations with high-accuracy orthonormal eigenvectors 9,031,34714/207,18611/15/2009PDFText Focus Correction
Variable focusing of electron microscopy image data utilizing fractional powers of the Fourier transform operator 8,934,73113/846,81002/25/1999
02/25/2000
09/18/2003
PDFText Focus Correction
Variable focusing of electron microscopy image data utilizing origin-centered discrete fractional fourier transform8,897,59013/846,76002/25/1999
02/25/2000
09/18/2003
PDFTextFocus Correction
High-Accuracy Centered Fractional Fourier Transform Matrix for Optical Imaging and Other Applications
8,712,185 13/959,604
11/15/2009 PDF
Text Focus Correction
Correction of Mis-focus in Recorded Images Using Centered Discrete Fractional Fourier Transformations with High-Accuracy Orthonormal Eigenvectors8,542,94512/945,90211/15/2009PDFTextFocus Correction
Generation of Image Data with Correction For Optical Misfocus Utilizing Fractional Powers of the Fourier Transform Operator 8,442,34213/346,61902/25/1999
02/25/2000
09/18/2003
PDFTextFocus Correction
Correction of Unfocus and  Misfocus via Origin-Centered Discrete Fractional Fourier Transform 8,442,34113/346,45904/11/2008PDFTextFocus Correction
Discrete Fractional Fourier Numerical Environments for Computer Modeling of Image Propagation Through a Physical Medium in Restoration and other Applications8,094,96913/037,34202/25/1999
02/25/2000
09/18/2003
PDFText Focus Correction
Generation of Image Data with Correction For Optical Misfocus Utilizing Fractional Powers of the Fourier Transform Operator8,094,96112/754,58702/25/1999
02/25/2000
PDFText Focus Correction
Focus Correction in Electron Microscope and Particle Beam Imaging Systems7,697,77711/929,36002/25/1999
02/25/2000
PDFText Focus Correction
Focus Correction Using Fractional Fourier Operator Approximations7,627,19511/697,62402/25/1999
02/25/2000
PDFText Focus Correction
Computing Arbitrary Fractional Powers Of A Transform Operator From Selected Precomputed Fractional Powers Of The Operator7,203,37710/937,19202/25/1999
02/25/2000
PDFText Focus Correction
Relative Optical Path Phase Reconstruction In The Correction Of Misfocused Images Using Fractional Powers Of The Fourier Transform7,054,50410/665,43902/25/1999
02/25/2000
PDFText Focus Correction
Iterative Approximation Environments for Modeling the Evolution of an Image Propagating Through a Physical Medium in Restoration and Other Applications

Iterative Approximation Environments for Modeling the Evolution of an Image Propagating Through a Physical Medium in Restoration and Other Applications

7,039,252


RE42,187
10/980,744


12/101,878
02/25/1999
02/25/2000
09/18/2003
02/25/1999
02/25/2000
09/18/2003
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Focus Correction


Focus Correction
Correction of Unfocused Lens Effects Via Fractional Fourier Transform6,687,41809/512,77502/25/1999PDFText Focus Correction

Pending Patents

TitlePublication NumberApplication NumberPriority DatesPDFText OnlyRelated Patents

Pending Unpublished Applications

TitleApplication NumberPriority DatesRelated Patents