New Renaissance Institute’s founder is credited as the first to discover and report the fractional Fourier transform properties of lenses described in the landmark text 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. This rarely-cited but occasionally recognized paper was accepted for presentation only as poster session at the 1988 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 this 1993-initiated fractional Fourier transform optics 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 light-field imaging and computational imaging, including its lensless light-field imaging camera work.
NRI is pleased to have hosted summer interns from U.C. Santa Cruz, U.C. Irvine, U.C. Berkeley, and U.C. San Diego who have provided detailed laboratory work for in this technology area.
Issued Patents
| Title | Patent Number | Application Number | Priority Dates | Text Only | Related Patents | |
|---|---|---|---|---|---|---|
| Correction of over-focus in digital images using centered discrete imaginary-power fractional Fourier transformations with high-accuracy orthonormal eigenvectors | 9,031,347 | 14/207,186 | 11/15/2009 | Text | Focus Correction |
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| Variable focusing of electron microscopy image data utilizing fractional powers of the Fourier transform operator | 8,934,731 | 13/846,810 | 02/25/1999 02/25/2000 09/18/2003 | Text | Focus Correction | |
| Variable focusing of electron microscopy image data utilizing origin-centered discrete fractional fourier transform | 8,897,590 | 13/846,760 | 02/25/1999 02/25/2000 09/18/2003 | Text | Focus 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 Eigenvectors | 8,542,945 | 12/945,902 | 11/15/2009 | Text | Focus Correction | |
| Generation of Image Data with Correction For Optical Misfocus Utilizing Fractional Powers of the Fourier Transform Operator | 8,442,342 | 13/346,619 | 02/25/1999 02/25/2000 09/18/2003 | Text | Focus Correction | |
| Correction of Unfocus and Misfocus via Origin-Centered Discrete Fractional Fourier Transform | 8,442,341 | 13/346,459 | 04/11/2008 | Text | Focus Correction | |
| Discrete Fractional Fourier Numerical Environments for Computer Modeling of Image Propagation Through a Physical Medium in Restoration and other Applications | 8,094,969 | 13/037,342 | 02/25/1999 02/25/2000 09/18/2003 | Text | Focus Correction | |
| Generation of Image Data with Correction For Optical Misfocus Utilizing Fractional Powers of the Fourier Transform Operator | 8,094,961 | 12/754,587 | 02/25/1999 02/25/2000 | Text | Focus Correction | |
| Computing Arbitrary Fractional Powers of a Transform Operator from Selected Precomputed Fractional Powers of the Operator | 7,697,777 | 11/929,360 | 02/25/1999 02/25/2000 | Text | Focus Correction | |
| Focus Correction Using Fractional Fourier Operator Approximations | 7,627,195 | 11/697,624 | 02/25/1999 02/25/2000 | Text | Focus Correction | |
| Computing Arbitrary Fractional Powers Of A Transform Operator From Selected Precomputed Fractional Powers Of The Operator | 7,203,377 | 10/937,192 | 02/25/1999 02/25/2000 | Text | Focus Correction | |
| Relative Optical Path Phase Reconstruction In The Correction Of Misfocused Images Using Fractional Powers Of The Fourier Transform | 7,054,504 | 10/665,439 | 02/25/1999 02/25/2000 | Text | 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 | PDF | Text Text | Focus Correction Focus Correction |
| Correction of Image Misfocus via Fractional Fourier Transform | 6,687,418 | 09/512,775 | 02/25/1999 | Text | Focus Correction |
Pending Published Applications
| Title | Publication Number | Application Number | Priority Dates | Publish Date | Text Only | Related Patents |
Pending Unpublished Applications
| Title | Application Number | Priority Dates | Related Patents |