Fourier transform holography using pseudo-random phase shifting of object illuminating beams and apodization

• US 4,013,338 A
• Filed: 01/26/1976
• Issued: 03/22/1977
• Est. Priority Date: 05/13/1975
• Status: Expired due to Term

• Current Assignee: Matsushita Electric Industrial Company Limited (Panasonic Holdings Corporation)
• Original Assignee: Matsushita Electric Industrial Company Limited (Panasonic Holdings Corporation)
• Inventors: Sato, Isao, Kato, Makoto
• Primary Examiner(s): Stern, Ronald J.
• Application Number:
  US05/652,154
• Time in Patent Office: 421 Days
• Field of Search: 350/3.5, 350/162 SF, 350/314, 340/173 LT, 340/173 LM
• US Class Current: 359/29
• CPC Class Codes: G03H 1/041 Optical element in the object space affecting the object beam, not otherwise provided for
• 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: G03H 2223/13 Phase mask
• CPC Class Codes: Y10S 359/90 Methods

Abstract

A phase mask comprised of a square array of phase shifting areas arranged in pseudo-random pattern is illuminated with a beam of electromagnetic radiation, as a result of which an array of pseudo-randomly phase shifted beams emerges from the phase mask and impinges upon an object transparency to be intensity-modulated thereby and come to a focus on a Fourier transform plane. The power spectrum of the beams distributes in orthogonal directions on the Fourier transform plane from its center maxima in a distinct pattern of series of fringes. The technique of apodization is employed to suppress the fringes to thereby reduce the coherent noise of a hologram to a minimum.

Claims

1. A system for forming a hologram of an array of beams of electromagnetic radiation on a Fourier transform plane, comprising:

a pseudo-random phase mask receptive in use of a beam of electromagnetic radiation and comprised of a plurality of phase shifting areas arranged in a pattern of rows and columns, there being an approximately equal number of phase shifting areas for each of the different phase shifts, wherein the number of different phase shifts is N which is greater than three inclusive and each of the different phase shifts is one of the multiples of m360°

/N, where m ranges from 1 to N, and the phase difference between orthogonally adjacent phase shifting areas is 360°

/N, whereby the power spectrum of each of said phase-shifted beams on the Fourier transform plane distributes in orthogonal directions from the center maximum of the power spectrum;

means for apodizing the phase-shifted beams; and

means for recording a Fourier transform hologram of said phase-shifted, apodized beams.

2. A system as claimed in claim 1, wherein said apodizing means comprises an aperture mask comprised of an array of apertures having one-to-one correspondence with the phase shifting areas of said phase mask, each of said apertures having a substantially Gaussian light transmission characteristic to impart a Gaussian intensity distribution to a beam passing therethrough.

3. A system as claimed in claim 2, wherein each of said apertures is square shaped and wherein the length of the edges thereof is equal to 2λ

f/D_H, wherein λ

is the wavelength of the beam, f is the focal length of a Fourier transform lens disposed between the pseudo-random phase mask and the recording means, and D_H is the length of edges of said Fourier transform hologram.

4. A system as claimed in claim 1, wherein said apodizing means is a filter disposed in front of said recording means.

5. A system as claimed in claim 1, wherein each of said phase shifting areas has a phase difference of 90°

with respect to orthogonally adjacent areas and phase differences of one of 0° and

180 °

with respect to orthogonally adjacent areas which adjoin the first mentioned orthogonally adjacent areas remote from said each of phase shifting areas.

6. A method for reconstructing a Fourier transform hologram, wherein said hologram is prepared by a method comprising the steps of directing a beam of electromagnetic radiation to a pseudo-random phase mask comprised of a plurality of phase shifting areas arranged in a pattern of rows and columns, there being an approximately different phase shifts, wherein the number of different phase shifts is N which is greater than three inclusive and each of the different phase shifts is one of the multiples of m360°

/N, where m ranges from 1 to N, and the phase difference between orthogonally adjacent phase shifting areas is 360°

/N, to produce a plurality of phase-shifted beams, placing an object transparency behind the phase mask in the direction of the beam to intensity-modulate the phase-shifted beams, subjecting a recording medium to the intensity-modulated, phase-shifted beams and directing a reference beam to said recording medium to produce an interference fringe pattern with said intensity-modulated, phase-shifted beams, said method comprising;

directing a beam of electromagnetic radiation to said hologram, said beam having a uniform intensity distribution across the transverse cross-section thereof; and

placing an apodization filter in the path of said beam to impart a substantially Gaussian intensity distribution to said beam.

7. A method for reconstructing a Fourier transform hologram, wherein said hologram is prepared by a method comprising the steps of directing a beam of electromagnetic radiation to a pseudo-random phase mask comprised of a plurality of phase shifting areas arranged in a pattern of rows and columns, there being an approximately equal number of phase shifting areas for each of the different phase shifts, wherein the number of different phase shifts is N which is greater than three inclusive and each of the different phase shifts is one of the multiples of m360°

/N, where m ranges from 1 to N, and the phase difference between orthogonally adjacent phase shifting areas is 360°

/N, to produce a plurality of phase-shifted beams, placing an object transparency behind the phase mask in the direction of the beam to intensity-modulate the phase-shifted beams, subjecting a recording medium to the intensity-modulated, phase-shifted beams and directing a reference beam to said recording medium to produce an interference fringe pattern with said intensity-modulated, phase-shifted beams, said method comprising,

directing a beam of electromagnetic radiation to said hologram, said beam having a substantially Gaussian intensity distribution across the transverse cross-section thereof.