Abstract

We propose and demonstrate parallel subtraction of the Fourier power spectrum of two images with the use of real-time holographic interferometry. The subtraction, which exhibits shift invariance, is achieved by employing a Mach–Zehnder interferometer and a photorefractive crystal. The results are presented and discussed.

© 1992 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. See, for example, J. F. Ebersole, Opt. Eng. 14, 436 (1975).
  2. P. Yeh, T. Y. Chang, P. H. Beckwith, Opt. Lett. 13, 586 (1988).
    [CrossRef] [PubMed]
  3. A. E. Chiou, P. Yeh, Opt. Lett. 11, 306 (1986).
    [CrossRef] [PubMed]
  4. S.-K. Kwong, G. A. Rakuljic, A. Yariv, Appl. Phys. Lett. 48, 201 (1986).
    [CrossRef]
  5. Y. Tomita, R. Yahalom, A. Yariv, Appl. Phys. Lett. 52, 425 (1988).
    [CrossRef]
  6. See, for example, P. Yeh, Optical Waves in Layered Media (Wiley, New York, 1988).
  7. H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1969).
  8. See, for example, J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

1988 (2)

P. Yeh, T. Y. Chang, P. H. Beckwith, Opt. Lett. 13, 586 (1988).
[CrossRef] [PubMed]

Y. Tomita, R. Yahalom, A. Yariv, Appl. Phys. Lett. 52, 425 (1988).
[CrossRef]

1986 (2)

A. E. Chiou, P. Yeh, Opt. Lett. 11, 306 (1986).
[CrossRef] [PubMed]

S.-K. Kwong, G. A. Rakuljic, A. Yariv, Appl. Phys. Lett. 48, 201 (1986).
[CrossRef]

1975 (1)

See, for example, J. F. Ebersole, Opt. Eng. 14, 436 (1975).

1969 (1)

H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1969).

Beckwith, P. H.

Chang, T. Y.

Chiou, A. E.

Ebersole, J. F.

See, for example, J. F. Ebersole, Opt. Eng. 14, 436 (1975).

Goodman, J. W.

See, for example, J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

Kogelnik, H.

H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1969).

Kwong, S.-K.

S.-K. Kwong, G. A. Rakuljic, A. Yariv, Appl. Phys. Lett. 48, 201 (1986).
[CrossRef]

Rakuljic, G. A.

S.-K. Kwong, G. A. Rakuljic, A. Yariv, Appl. Phys. Lett. 48, 201 (1986).
[CrossRef]

Tomita, Y.

Y. Tomita, R. Yahalom, A. Yariv, Appl. Phys. Lett. 52, 425 (1988).
[CrossRef]

Yahalom, R.

Y. Tomita, R. Yahalom, A. Yariv, Appl. Phys. Lett. 52, 425 (1988).
[CrossRef]

Yariv, A.

Y. Tomita, R. Yahalom, A. Yariv, Appl. Phys. Lett. 52, 425 (1988).
[CrossRef]

S.-K. Kwong, G. A. Rakuljic, A. Yariv, Appl. Phys. Lett. 48, 201 (1986).
[CrossRef]

Yeh, P.

Appl. Phys. Lett. (2)

S.-K. Kwong, G. A. Rakuljic, A. Yariv, Appl. Phys. Lett. 48, 201 (1986).
[CrossRef]

Y. Tomita, R. Yahalom, A. Yariv, Appl. Phys. Lett. 52, 425 (1988).
[CrossRef]

Bell Syst. Tech. J. (1)

H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1969).

Opt. Eng. (1)

See, for example, J. F. Ebersole, Opt. Eng. 14, 436 (1975).

Opt. Lett. (2)

Other (2)

See, for example, P. Yeh, Optical Waves in Layered Media (Wiley, New York, 1988).

See, for example, J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1

Schematic of a double Mach–Zehnder holographic interferometer.

Fig. 2
Fig. 2

Subtraction of Fourier power spectra, (a) Patterns 1 and 2, whose Fourier power spectra are to be subtracted. (b) Fourier power spectrum of pattern 1 (upper image) and the subtraction of Fourier power spectra of patterns 1 and 2 (lower image).

Fig. 3
Fig. 3

Locations of the detectors for measuring the second component of the horizontal (H) and the second component of the vertical (V) Fourier spectrum.

Fig. 4
Fig. 4

Output power of the second vertical Fourier component as a function of the displacement. The quality of shift invariance is measured by shifting pattern 2 both (a) horizontally and (b) vertically.

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

I ( x , y ) = | r 1 exp ( i k 1 r ) + t 1 exp ( i k 2 r ) | 2 + | t 2 exp ( i k 1 r ) + r 2 exp ( i k 2 r ) | 2 , = | 1 | 2 + | 2 | 2 + { ( r * t | 1 | 2 + r t * | 2 | 2 ) × exp [ i ( k 2 k 1 ) r ] + c . c . } ,
Δ n | 1 | 2 | 2 | 2 I 0 exp [ i ( k 2 k 1 ) r ] + c . c . ,
Δ θ Δ x f λ L sin θ ,
g ( x , y ) f ( x , y ) exp [ i 2 π d λ d 1 d 2 ( x x + y y ) ] × exp [ i π λ d 1 ( x 2 + y 2 ) ( 1 d d 1 ) ] × exp [ i π λ d 2 ( x 2 + y 2 ) ( 1 d d 2 ) ] d x d y ,
1 d = 1 d 1 + 1 d 2 1 f .
( a f ) 2 L λ 1 ,

Metrics