Fractional Fourier Optical Processing

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, and visible-light imaging.
The items below pertain to NRI’s work in the area of fractional Fourier transforms in monolithic and other forms of optical computation engines. Related work in some of the underlying mathematics has been performed in roughly the same time frame at Bilkent University in Ankara, Turkey.

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
Programmable optical computing device employing LED array transducers, non-quadratic phase optical elements, and stacked light modulator elements 8,792,16714/019,28402/25/1999PDFText Fractional Fourier Optical Processing
Monolithic or Hybrid Integrated Optical Information Processor Employing a Plurality of Controllable Optical Transfer Functions at Fractional Fourier Planes8,553,32913/450,35702/25/1999PDFTextFractional Fourier Optical Processing
Programmable Optical Computing Device Employing LED Array Transducers And Stacked Light Modulator Elements in Fractional Fourier Planes8,164,83213/049,74902/25/1999PDFText Fractional Fourier Optical Processing
Programmable Optical Processing Device Employing Stacked Controllable Phase-Shifting Elements in Fractional Fourier Planes7,911,69812/560,32702/25/1999PDFText Fractional Fourier Optical Processing
Programmable Optical Processing Device Employing Stacked Light Modulator Elements in Fractional Fourier Planes7,609,44711/929,25902/25/1999PDFText Fractional Fourier Optical Processing
Programmable Optical Processing Device Employing Multiple Controllable Light Modulator Elements in Fractional Fourier Transform Planes7,391,57011/294,68502/25/1999PDFText Fractional Fourier Optical Processing
Non-Positive-Definite Optical Filtering From Positive-Definite Transfer Functions6,972,90510/656,34202/25/1999PDFText Fractional Fourier Optical Processing
Image Processing Utilizing Non-Positive-Definite Transfer Functions Via Fractional Fourier Transform6,650,47609/512,78102/25/1999PDFText Fractional Fourier Optical Processing

Pending Published Applications

TitlePublication NumberApplication NumberPriority DatesPublish DatePDFText OnlyRelated Patents

Pending Unpublished Applications

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