FOURIER TRANSFORM RECORDING WITH RANDOM PHASE SHIFTING

• US 3,604,778 A
• Filed: 10/22/1969
• Issued: 09/14/1971
• Est. Priority Date: 10/22/1969
• Status: Expired due to Term

• Current Assignee: Christoph B. Burckhardt
• Original Assignee: Christoph B. Burckhardt
• Inventors: Burckhardt, Christoph B.
• Primary Examiner(s): Schonberg, David
• Assistant Examiner(s): Stern, Ronald J.
• Application Number:
  US04/868,485
• Time in Patent Office: 692 Days
• Field of Search: 350/3.5 96/27R,27E,27H 346/107,108,45.2
• US Class Current: 359/29
• CPC Class Codes: G03H 1/16 using Fourier transform G03H1/10, G03H1/12, G03H1/14 take precedence; analogue computers G06G, e.g. G06G7/19
• CPC Class Codes: G06E 3/001 Analogue devices in which mathematical operations are carried out with the aid of optical or electro-optical elements optical elements per se G02B; devices consisting of a plurality of solid state components, including light sensitive semiconductor components, formed in or on a common substrate H01L27/14; electro-, magneto- or acousto-optics, non-linear optics G02F1/00; graph reading G06K11/00

Abstract

In making a record of the exact Fourier transform of an array of beams of electromagnetic radiation, the phase of each of a substantial fraction of the beams is shifted by a constant amount before recording the transform.

Claims

1. Apparatus for forming a record of the Fourier transform of an array of beams of electromagnetic radiation, comprising:

means for forming an array of beams of electromagnetic radiation, means for shifting the phase of at least one-third of the beams in the array by an amount that is at least ninety degrees and is substantially constant across each beam, wherein the beams that are phase shifted are distributed approximately randomly throughout said array and means for recording the Fourier transform of the beams.

2. The apparatus of claim 1 wherein the probability that a particular beam is phase shifted ranges from approximately one-third to approximately two-thirds.

3. The apparatus of claim 1 wherein the amount of phase shift is the same for all the phase-shifted beams and ranges from approximately 140* to approximately 220* with respect to the beams that are not phase shifted.

4. The apparatus of claim 3 wherein:

the probability that a particular beam is phase shifted ranges from approximately two-fifths to approximately three-fifths, the record of the Fourier transform is a Fourier transform hologram, the beams of electromagnetic radiation have a constant phase relation with a reference beam with which they interfere to form the hologram, and the beams of electromagnetic radiation are disposed in an ordered array.

5. The apparatus of claim 4 wherein the amount of phase shift is approximately 180* and the probability that a particular beam is phase shifted is approximately one-half.

6. The apparatus of claim 4 wherein the means for shifting the phase of the beams is a phase mask comprised of an ordered array of phase-shifting areas that have a one-to-one correspondence with the ordered array of beams of electromagnetic radiation.

7. The apParatus of claim 6 wherein the phase mask is a glass slide in which the phase-shifting areas have been etched.

8. The apparatus of claim 1 wherein:

the phase shift in at least some of the phase-shifted beams is different from the phase shift in some of the other phase-shifted beams, the means for shifting the phase of the beams is a phase mask comprised of an array of phase-shifting areas that have a one-to-one correspondence with the array of beams of radiation, there being an approximately equal number of phase-shifting areas for each of the different phase shifts that are effected.

9. The apparatus of claim 8 wherein the number of different phase shifts is (N-1) and each of the different phase shifts that can be effected in the phase-shifted beams of radiation is one of the multiples of n360/N where n ranges from 1 to (N-1).