Abstract

A quad-phase-only filter (QPOF) is introduced. It is shown that the QPOF can have improved correlation response and signal-to-noise ratio with respect to the Hartley binary phase-only filter for some objects.

© 1989 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. D. Psaltis, E. G. Paek, S. S. Venkatesh, “Optical Image Correlation with a Binary Spatial Light Modulator,” Opt. Eng. 23, 698–704 (1984).
    [CrossRef]
  2. J. L. Horner, J. Leger, “Pattern Recognition with Binary Phase-Only Filters,” Appl. Opt. 24, 609–611 (1985).
    [CrossRef] [PubMed]
  3. J. L. Horner, H. O. Bartelt, “Two-Bit Correlation,” Appl. Opt. 24, 2889–2893 (1985).
    [CrossRef] [PubMed]
  4. D. M. Cottrell, R. A. Lilly, J. A. Davis, T. Day, “Optical Correlator Performance of Binary Phase-Only Filters Using Fourier and Hartley Transforms,” Appl. Opt. 26, 3755–3761 (1987).
    [CrossRef] [PubMed]
  5. F. M. Dickey, K. T. Stalker, J. J. Mason, “Bandwidth Considerations for Binary Phase-Only Filters,” Appl. Opt. 27, 3811–3818 (1988).
    [CrossRef] [PubMed]
  6. R. Kallman, “Optimal Low Noise Phase-Only and Binary Phase-Only Optical Correlation Filters for Threshold Detectors,” Appl. Opt. 25, 4216–4217 (1986).
    [CrossRef] [PubMed]
  7. F. M. Dickey, J. J. Mason, K. T. Stalker, “Analysis of Binarized Hartley Phase-Only Filter Performance with Respect to Stochastic Noise,” Proc. Soc. Photo-Opt. Instrum. Eng. 938, 2000 (1988), and Opt. Eng. 28, 8–13 (1989).
  8. D. L. Flannery, J. S. Loomis, M. E. Mitkovich, “Design Elements of Binary Phase-Only Correlation Filters,” Appl. Opt. 27, 4231–4235 (1988).
    [CrossRef] [PubMed]
  9. B. V. K. Vijaya Kumar, Z. Bahri, “Phase-Only Filters with Improved Signal to Noise Ratio,” Appl. Opt. 28, 250–257 (1989).
    [CrossRef]
  10. B. D. Hansche, J. J. Mason, F. M. Dickey, “Quad-Phase-Only Filter Implementation,” submitted to Appl. Opt.

1989 (1)

1988 (3)

F. M. Dickey, K. T. Stalker, J. J. Mason, “Bandwidth Considerations for Binary Phase-Only Filters,” Appl. Opt. 27, 3811–3818 (1988).
[CrossRef] [PubMed]

D. L. Flannery, J. S. Loomis, M. E. Mitkovich, “Design Elements of Binary Phase-Only Correlation Filters,” Appl. Opt. 27, 4231–4235 (1988).
[CrossRef] [PubMed]

F. M. Dickey, J. J. Mason, K. T. Stalker, “Analysis of Binarized Hartley Phase-Only Filter Performance with Respect to Stochastic Noise,” Proc. Soc. Photo-Opt. Instrum. Eng. 938, 2000 (1988), and Opt. Eng. 28, 8–13 (1989).

1987 (1)

1986 (1)

1985 (2)

1984 (1)

D. Psaltis, E. G. Paek, S. S. Venkatesh, “Optical Image Correlation with a Binary Spatial Light Modulator,” Opt. Eng. 23, 698–704 (1984).
[CrossRef]

Bahri, Z.

Bartelt, H. O.

Cottrell, D. M.

Davis, J. A.

Day, T.

Dickey, F. M.

F. M. Dickey, K. T. Stalker, J. J. Mason, “Bandwidth Considerations for Binary Phase-Only Filters,” Appl. Opt. 27, 3811–3818 (1988).
[CrossRef] [PubMed]

F. M. Dickey, J. J. Mason, K. T. Stalker, “Analysis of Binarized Hartley Phase-Only Filter Performance with Respect to Stochastic Noise,” Proc. Soc. Photo-Opt. Instrum. Eng. 938, 2000 (1988), and Opt. Eng. 28, 8–13 (1989).

B. D. Hansche, J. J. Mason, F. M. Dickey, “Quad-Phase-Only Filter Implementation,” submitted to Appl. Opt.

Flannery, D. L.

Hansche, B. D.

B. D. Hansche, J. J. Mason, F. M. Dickey, “Quad-Phase-Only Filter Implementation,” submitted to Appl. Opt.

Horner, J. L.

Kallman, R.

Leger, J.

Lilly, R. A.

Loomis, J. S.

Mason, J. J.

F. M. Dickey, K. T. Stalker, J. J. Mason, “Bandwidth Considerations for Binary Phase-Only Filters,” Appl. Opt. 27, 3811–3818 (1988).
[CrossRef] [PubMed]

F. M. Dickey, J. J. Mason, K. T. Stalker, “Analysis of Binarized Hartley Phase-Only Filter Performance with Respect to Stochastic Noise,” Proc. Soc. Photo-Opt. Instrum. Eng. 938, 2000 (1988), and Opt. Eng. 28, 8–13 (1989).

B. D. Hansche, J. J. Mason, F. M. Dickey, “Quad-Phase-Only Filter Implementation,” submitted to Appl. Opt.

Mitkovich, M. E.

Paek, E. G.

D. Psaltis, E. G. Paek, S. S. Venkatesh, “Optical Image Correlation with a Binary Spatial Light Modulator,” Opt. Eng. 23, 698–704 (1984).
[CrossRef]

Psaltis, D.

D. Psaltis, E. G. Paek, S. S. Venkatesh, “Optical Image Correlation with a Binary Spatial Light Modulator,” Opt. Eng. 23, 698–704 (1984).
[CrossRef]

Stalker, K. T.

F. M. Dickey, K. T. Stalker, J. J. Mason, “Bandwidth Considerations for Binary Phase-Only Filters,” Appl. Opt. 27, 3811–3818 (1988).
[CrossRef] [PubMed]

F. M. Dickey, J. J. Mason, K. T. Stalker, “Analysis of Binarized Hartley Phase-Only Filter Performance with Respect to Stochastic Noise,” Proc. Soc. Photo-Opt. Instrum. Eng. 938, 2000 (1988), and Opt. Eng. 28, 8–13 (1989).

Venkatesh, S. S.

D. Psaltis, E. G. Paek, S. S. Venkatesh, “Optical Image Correlation with a Binary Spatial Light Modulator,” Opt. Eng. 23, 698–704 (1984).
[CrossRef]

Vijaya Kumar, B. V. K.

Appl. Opt. (7)

Opt. Eng. (1)

D. Psaltis, E. G. Paek, S. S. Venkatesh, “Optical Image Correlation with a Binary Spatial Light Modulator,” Opt. Eng. 23, 698–704 (1984).
[CrossRef]

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

F. M. Dickey, J. J. Mason, K. T. Stalker, “Analysis of Binarized Hartley Phase-Only Filter Performance with Respect to Stochastic Noise,” Proc. Soc. Photo-Opt. Instrum. Eng. 938, 2000 (1988), and Opt. Eng. 28, 8–13 (1989).

Other (1)

B. D. Hansche, J. J. Mason, F. M. Dickey, “Quad-Phase-Only Filter Implementation,” submitted to Appl. Opt.

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.


Equations (10)

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

H Q ( ω ) = sgn [ G e ( ω ) ] + i sgn [ G o ( ω ) ] ,
C Q ( x ) = 1 16 π 4 | Δ ω G ( ω ) H Q ( ω ) exp ( i ω · x ) d 2 ω | 2 = 1 16 π 4 | Δ ω [ G e ( ω ) i G o ( ω ) ] × [ sgn G e ( ω ) + i sgn G o ( ω ) ] exp ( i ω · x ) d 2 ω | 2 = 1 16 π 4 | Δ ω { | G e ( ω ) | + | G o ( ω ) | + i [ G e ( ω ) sgn G o ( ω ) G o ( ω ) sgn G e ( ω ) ] } · exp ( i ω · x ) d 2 ω | 2 ,
SNR QPOF = C Q ( 0 ) 1 4 π 2 Δ ω 2 P n ( ω ) d 2 ω ,
| H Q ( ω ) | 2 = | sgn [ F e ( ω ) ] + i sgn [ F o ( ω ) ] | 2 = 2 .
C Q ( 0 ) = 1 16 π 2 | Δ ω [ | G e ( ω ) | + | G o ( ω ) | ] d 2 ω | 2 .
C H ( 0 ) = 1 16 π 2 [ Δ ω | G e ( ω ) | S ( ω ) d 2 ω ] 2 + 1 16 π 4 { Δ ω | G o ( ω ) | [ 1 S ( ω ) ] d 2 ω } 2 ,
S ( ω ) = { 1 , | F e ( ω ) | | F o ( ω ) | , 0 , otherwise .
F ( ω ) W ( cos ω x o i sin ω x o ) ,
SNR Q SNR H = C Q ( 0 ) 2 C H ( 0 ) .
SNR Q SNR H = [ 0 π / 2 x 0 ( | cos ω x 0 | + | sin ω x 0 | ) d ω ] 2 2 [ ( 0 π / 4 x 0 | cos ω x 0 | d ω ) 2 + ( π / 4 x 0 π / 2 x 0 | sin ω x 0 | d ω ) 2 ] 2 = 2 .

Metrics