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, 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

Title | Patent Number | Application Number | Priority Dates | Text Only | Related Patents | |
---|---|---|---|---|---|---|

Monolithic or Hybrid Integrated Optical Information Processor Employing a Plurality of Controllable Optical Transfer Functions at Fractional Fourier Planes | 8,553,329 | 13/450,357 | 02/25/1999 | Text | Fractional Fourier Optical Processing | |

Programmable Optical Computing Device Employing LED Array Transducers And Stacked Light Modulator Elements in Fractional Fourier Planes | 8,164,832 | 13/049,749 | 02/25/1999 | Text | Fractional Fourier Optical Processing | |

Programmable Optical Processing Device Employing Stacked Controllable Phase-Shifting Elements in Fractional Fourier Planes | 7,911,698 | 12/560,327 | 02/25/1999 | Text | Fractional Fourier Optical Processing | |

Programmable Optical Processing Device Employing Stacked Light Modulator Elements in Fractional Fourier Planes | 7,609,447 | 11/929,259 | 02/25/1999 | Text | Fractional Fourier Optical Processing | |

Programmable Optical Processing Device Employing Multiple Controllable Light Modulator Elements in Fractional Fourier Transform Planes | 7,391,570 | 11/294,685 | 02/25/1999 | Text | Fractional Fourier Optical Processing | |

Non-Positive-Definite Optical Filtering From Positive-Definite Transfer Functions | 6,972,905 | 10/656,342 | 02/25/1999 | Text | Fractional Fourier Optical Processing | |

Image Processing Utilization Non-Positive-Definite Transfer Functions Via Fractional Fourier Transform | 6,650,476 | 09/512,781 | 02/25/1999 | Text | Fractional Fourier Optical Processing |

## Pending Patents

Title | Publication Number | Application Number | Priority Dates | Text Only | Related Patents |

## Pending Unpublished Applications

Title | Application Number | Priority Dates | Related Patents |
---|---|---|---|

Programmable Optical Computing Device Employing LED Array Transducers, Non-Quadratic Phase Optical Elements, and Stacked LightModulator Elements | 14/335,799 | 02/25/1999 | Fractional Fourier Optical Processing |