Abstract

Previously, we had proposed a hybrid opto-electronic correlator (HOC), which can achieve the same functionality as that of a holographic optical correlator but without using any holographic medium. Here, we demonstrate experimentally that the HOC is capable of detecting objects in a scale, rotation, and shift invariant manner. First, the polar Mellin transformed (PMT) versions of two images are produced, using a combination of optical and electronic signal processing. The PMT images are then used as the reference and the query inputs for the HOC. The observed correlation signal is used to infer, with high accuracy, the relative scale and angular orientation of the original images. We also discuss practical constraints in reaching a high-speed implementation of such a system. In addition, we describe how these challenges may be overcome for producing an automated version of such a correlator.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. A. Vander Lugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory 10(2), 139–145 (1964).
    [Crossref]
  2. A. Heifetz, J. T. Shen, J.-K. Lee, and M. S. Shahriar, “Translation-invariant object recognition system using an optical correlator and a super-parallel holographic random access memory,” Opt. Eng. 45, 025201 (2006).
  3. A. Heifetz, G. S. Pati, J. T. Shen, J. K. Lee, M. S. Shahriar, C. Phan, and M. Yamamoto, “Shift-invariant real-time edge-enhanced VanderLugt correlator using video-rate compatible photorefractive polymer,” Appl. Opt. 45(24), 6148–6153 (2006).
    [Crossref] [PubMed]
  4. Q. Tang and B. Javidi, “Multiple-object detection with a chirp-encoded joint transform correlator,” Appl. Opt. 32(26), 5079–5088 (1993).
    [Crossref] [PubMed]
  5. J. Khoury, M. Cronin-golomb, P. Gianino, and C. Woods, “Photorefractive two-beam-coupling nonlinear joint-transform correlator,” J. Opt. Soc. Am. B 11(11), 2167–2174 (1994).
    [Crossref]
  6. B. Javidi, J. Li, and Q. Tang, “Optical implementation of neural networks for face recognition by the use of nonlinear joint transform correlators,” Appl. Opt. 34(20), 3950–3962 (1995).
    [Crossref] [PubMed]
  7. F. T. S. Yu and X. J. Lu, “A real-time programmable joint transform correlator,” Opt. Commun. 52(1), 10–16 (1984).
    [Crossref]
  8. M. S. Shahriar, R. Tripathi, M. Kleinschmit, J. Donoghue, W. Weathers, M. Huq, and J. T. Shen, “Superparallel holographic correlator for ultrafast database searches,” Opt. Lett. 28(7), 525–527 (2003).
    [Crossref] [PubMed]
  9. F. Lei, M. Iton, and T. Yatagai, “Adaptive binary joint transform correlator for image recognition,” Appl. Opt. 41(35), 7416–7421 (2002).
    [Crossref] [PubMed]
  10. D. A. Gregory, J. A. Loudin, and H.-K. Liu, “Joint transform correlator limitations,” Proc. SPIE1053, 198–207 (1989).
  11. B. Javidi and C.-J. Kuo, “Joint transform image correlation using a binary spatial light modulator at the Fourier plane,” Appl. Opt. 27(4), 663–665 (1988).
    [PubMed]
  12. M. S. Monjur, S. Tseng, R. Tripathi, J. J. Donoghue, and M. S. Shahriar, “Hybrid optoelectronic correlator architecture for shift-invariant target recognition,” J. Opt. Soc. Am. A 31(1), 41–47 (2014).
    [Crossref] [PubMed]
  13. M. S. Monjur, S. Tseng, M. F. Fouda, and S. M. Shahriar, “Experimental demonstration of the hybrid opto-electronic correlator for target recognition,” Appl. Opt. 56(10), 2754–2759 (2017).
    [Crossref] [PubMed]
  14. D. Casasent and D. Psaltis, “Position, rotation, and scale invariant optical correlation,” Appl. Opt. 15(7), 1795–1799 (1976).
    [Crossref] [PubMed]
  15. D. Casasent and D. Psaltis, “Scale invariant optical correlation using Mellin transforms,” Opt. Commun. 17(1), 59–63 (1976).
    [Crossref]
  16. D. Casasent and D. Psaltis, “New optical transforms for pattern recognition,” Proc. IEEE 65(1), 77–84 (1977).
    [Crossref]
  17. D. Asselin and H. H. Arsenault, “Rotation and scale invariance with polar and log-polar coordinate transformations,” Opt. Commun. 104(4-6), 391–404 (1994).
    [Crossref]
  18. D. Sazbon, Z. Zalevsky, E. Rivlin, and D. Mendlovic, “Using Fourier/Mellin-based correlators and their fractional versions in navigational tasks,” Pattern Recognit. 35(12), 2993–2999 (2002).
    [Crossref]
  19. M. S. Monjur, S. Tseng, R. Tripathi, and M. S. Shahriar, “Incorporation of polar Mellin transform in a hybrid optoelectronic correlator for scale and rotation invariant target recognition,” J. Opt. Soc. Am. A 31(6), 1259–1272 (2014).
    [Crossref] [PubMed]
  20. W. Shi, J. Caballero, F. Huszár, J. Totz, A. Aitken, R. Bishop, D. Rueckert, and Z. Wang, “Real-Time Single Image and Video Super-Resolution Using an Efficient Sub-Pixel Convolutional Neural Network,” in IEEE Conference on Computer Vision and Pattern Recognition (CVPR) (2016), 1874–1883.
    [Crossref]
  21. M. Noskov, V. Tutatchikov, M. Lapchik, M. Ragulina, and T. Yamskikh, “Application of parallel version two-dimensional fast Fourier transform algorithm, analog of the Cooley-Tukey algorithm, for digital image processing of satellite data,” in E3S Web of Conferences (EDP Sciences, 2019), paper 01012.
  22. G. W. Li, S. J. Huang, H. S. Wu, S. Fang, D. S. Hong, T. Mohamed, and D. J. Han, “A Michelson interferometer for relative phase locking of optical beams,” J. Phys. Soc. Japan 77, 024301 (2008).
  23. B. W. Shiau, T. P. Ku, and D. J. Han, “Real-time phase difference control of optical beams using a mach-zehnder interferometer,” J. Phys. Soc. Japan 79, 034302 (2010).
  24. M. Lu, H. C. Park, E. Bloch, L. A. Johansson, M. J. Rodwell, and L. A. Coldren, “An integrated heterodyne optical phase-locked loop with record offset locking frequency,” in Optical Fiber Communication Conference OSA Technical Digest Series (Optical Society of America, 2014), paper Tu2H.4.
  25. Because the PZT is an electro-mechanical device, it requires a voltage source and a control circuit that introduce electrical noise into the system. A PID controller allows the PZT to maintain a more stable position. However, PID systems require a feedback loop. An MZI was constructed to provide the feedback for the PID via interferometry. This constitutes a mechanically controlled OPLL. This would not be required in an integrated system where the functionality of the PZT may be replaced by other means of phase control.

2017 (1)

2014 (2)

2010 (1)

B. W. Shiau, T. P. Ku, and D. J. Han, “Real-time phase difference control of optical beams using a mach-zehnder interferometer,” J. Phys. Soc. Japan 79, 034302 (2010).

2008 (1)

G. W. Li, S. J. Huang, H. S. Wu, S. Fang, D. S. Hong, T. Mohamed, and D. J. Han, “A Michelson interferometer for relative phase locking of optical beams,” J. Phys. Soc. Japan 77, 024301 (2008).

2006 (2)

A. Heifetz, G. S. Pati, J. T. Shen, J. K. Lee, M. S. Shahriar, C. Phan, and M. Yamamoto, “Shift-invariant real-time edge-enhanced VanderLugt correlator using video-rate compatible photorefractive polymer,” Appl. Opt. 45(24), 6148–6153 (2006).
[Crossref] [PubMed]

A. Heifetz, J. T. Shen, J.-K. Lee, and M. S. Shahriar, “Translation-invariant object recognition system using an optical correlator and a super-parallel holographic random access memory,” Opt. Eng. 45, 025201 (2006).

2003 (1)

2002 (2)

D. Sazbon, Z. Zalevsky, E. Rivlin, and D. Mendlovic, “Using Fourier/Mellin-based correlators and their fractional versions in navigational tasks,” Pattern Recognit. 35(12), 2993–2999 (2002).
[Crossref]

F. Lei, M. Iton, and T. Yatagai, “Adaptive binary joint transform correlator for image recognition,” Appl. Opt. 41(35), 7416–7421 (2002).
[Crossref] [PubMed]

1995 (1)

1994 (2)

D. Asselin and H. H. Arsenault, “Rotation and scale invariance with polar and log-polar coordinate transformations,” Opt. Commun. 104(4-6), 391–404 (1994).
[Crossref]

J. Khoury, M. Cronin-golomb, P. Gianino, and C. Woods, “Photorefractive two-beam-coupling nonlinear joint-transform correlator,” J. Opt. Soc. Am. B 11(11), 2167–2174 (1994).
[Crossref]

1993 (1)

1988 (1)

1984 (1)

F. T. S. Yu and X. J. Lu, “A real-time programmable joint transform correlator,” Opt. Commun. 52(1), 10–16 (1984).
[Crossref]

1977 (1)

D. Casasent and D. Psaltis, “New optical transforms for pattern recognition,” Proc. IEEE 65(1), 77–84 (1977).
[Crossref]

1976 (2)

D. Casasent and D. Psaltis, “Scale invariant optical correlation using Mellin transforms,” Opt. Commun. 17(1), 59–63 (1976).
[Crossref]

D. Casasent and D. Psaltis, “Position, rotation, and scale invariant optical correlation,” Appl. Opt. 15(7), 1795–1799 (1976).
[Crossref] [PubMed]

1964 (1)

A. Vander Lugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory 10(2), 139–145 (1964).
[Crossref]

Aitken, A.

W. Shi, J. Caballero, F. Huszár, J. Totz, A. Aitken, R. Bishop, D. Rueckert, and Z. Wang, “Real-Time Single Image and Video Super-Resolution Using an Efficient Sub-Pixel Convolutional Neural Network,” in IEEE Conference on Computer Vision and Pattern Recognition (CVPR) (2016), 1874–1883.
[Crossref]

Arsenault, H. H.

D. Asselin and H. H. Arsenault, “Rotation and scale invariance with polar and log-polar coordinate transformations,” Opt. Commun. 104(4-6), 391–404 (1994).
[Crossref]

Asselin, D.

D. Asselin and H. H. Arsenault, “Rotation and scale invariance with polar and log-polar coordinate transformations,” Opt. Commun. 104(4-6), 391–404 (1994).
[Crossref]

Bishop, R.

W. Shi, J. Caballero, F. Huszár, J. Totz, A. Aitken, R. Bishop, D. Rueckert, and Z. Wang, “Real-Time Single Image and Video Super-Resolution Using an Efficient Sub-Pixel Convolutional Neural Network,” in IEEE Conference on Computer Vision and Pattern Recognition (CVPR) (2016), 1874–1883.
[Crossref]

Bloch, E.

M. Lu, H. C. Park, E. Bloch, L. A. Johansson, M. J. Rodwell, and L. A. Coldren, “An integrated heterodyne optical phase-locked loop with record offset locking frequency,” in Optical Fiber Communication Conference OSA Technical Digest Series (Optical Society of America, 2014), paper Tu2H.4.

Caballero, J.

W. Shi, J. Caballero, F. Huszár, J. Totz, A. Aitken, R. Bishop, D. Rueckert, and Z. Wang, “Real-Time Single Image and Video Super-Resolution Using an Efficient Sub-Pixel Convolutional Neural Network,” in IEEE Conference on Computer Vision and Pattern Recognition (CVPR) (2016), 1874–1883.
[Crossref]

Casasent, D.

D. Casasent and D. Psaltis, “New optical transforms for pattern recognition,” Proc. IEEE 65(1), 77–84 (1977).
[Crossref]

D. Casasent and D. Psaltis, “Scale invariant optical correlation using Mellin transforms,” Opt. Commun. 17(1), 59–63 (1976).
[Crossref]

D. Casasent and D. Psaltis, “Position, rotation, and scale invariant optical correlation,” Appl. Opt. 15(7), 1795–1799 (1976).
[Crossref] [PubMed]

Coldren, L. A.

M. Lu, H. C. Park, E. Bloch, L. A. Johansson, M. J. Rodwell, and L. A. Coldren, “An integrated heterodyne optical phase-locked loop with record offset locking frequency,” in Optical Fiber Communication Conference OSA Technical Digest Series (Optical Society of America, 2014), paper Tu2H.4.

Cronin-golomb, M.

Donoghue, J.

Donoghue, J. J.

Fang, S.

G. W. Li, S. J. Huang, H. S. Wu, S. Fang, D. S. Hong, T. Mohamed, and D. J. Han, “A Michelson interferometer for relative phase locking of optical beams,” J. Phys. Soc. Japan 77, 024301 (2008).

Fouda, M. F.

Gianino, P.

Gregory, D. A.

D. A. Gregory, J. A. Loudin, and H.-K. Liu, “Joint transform correlator limitations,” Proc. SPIE1053, 198–207 (1989).

Han, D. J.

B. W. Shiau, T. P. Ku, and D. J. Han, “Real-time phase difference control of optical beams using a mach-zehnder interferometer,” J. Phys. Soc. Japan 79, 034302 (2010).

G. W. Li, S. J. Huang, H. S. Wu, S. Fang, D. S. Hong, T. Mohamed, and D. J. Han, “A Michelson interferometer for relative phase locking of optical beams,” J. Phys. Soc. Japan 77, 024301 (2008).

Heifetz, A.

A. Heifetz, J. T. Shen, J.-K. Lee, and M. S. Shahriar, “Translation-invariant object recognition system using an optical correlator and a super-parallel holographic random access memory,” Opt. Eng. 45, 025201 (2006).

A. Heifetz, G. S. Pati, J. T. Shen, J. K. Lee, M. S. Shahriar, C. Phan, and M. Yamamoto, “Shift-invariant real-time edge-enhanced VanderLugt correlator using video-rate compatible photorefractive polymer,” Appl. Opt. 45(24), 6148–6153 (2006).
[Crossref] [PubMed]

Hong, D. S.

G. W. Li, S. J. Huang, H. S. Wu, S. Fang, D. S. Hong, T. Mohamed, and D. J. Han, “A Michelson interferometer for relative phase locking of optical beams,” J. Phys. Soc. Japan 77, 024301 (2008).

Huang, S. J.

G. W. Li, S. J. Huang, H. S. Wu, S. Fang, D. S. Hong, T. Mohamed, and D. J. Han, “A Michelson interferometer for relative phase locking of optical beams,” J. Phys. Soc. Japan 77, 024301 (2008).

Huq, M.

Huszár, F.

W. Shi, J. Caballero, F. Huszár, J. Totz, A. Aitken, R. Bishop, D. Rueckert, and Z. Wang, “Real-Time Single Image and Video Super-Resolution Using an Efficient Sub-Pixel Convolutional Neural Network,” in IEEE Conference on Computer Vision and Pattern Recognition (CVPR) (2016), 1874–1883.
[Crossref]

Iton, M.

Javidi, B.

Johansson, L. A.

M. Lu, H. C. Park, E. Bloch, L. A. Johansson, M. J. Rodwell, and L. A. Coldren, “An integrated heterodyne optical phase-locked loop with record offset locking frequency,” in Optical Fiber Communication Conference OSA Technical Digest Series (Optical Society of America, 2014), paper Tu2H.4.

Khoury, J.

Kleinschmit, M.

Ku, T. P.

B. W. Shiau, T. P. Ku, and D. J. Han, “Real-time phase difference control of optical beams using a mach-zehnder interferometer,” J. Phys. Soc. Japan 79, 034302 (2010).

Kuo, C.-J.

Lapchik, M.

M. Noskov, V. Tutatchikov, M. Lapchik, M. Ragulina, and T. Yamskikh, “Application of parallel version two-dimensional fast Fourier transform algorithm, analog of the Cooley-Tukey algorithm, for digital image processing of satellite data,” in E3S Web of Conferences (EDP Sciences, 2019), paper 01012.

Lee, J. K.

Lee, J.-K.

A. Heifetz, J. T. Shen, J.-K. Lee, and M. S. Shahriar, “Translation-invariant object recognition system using an optical correlator and a super-parallel holographic random access memory,” Opt. Eng. 45, 025201 (2006).

Lei, F.

Li, G. W.

G. W. Li, S. J. Huang, H. S. Wu, S. Fang, D. S. Hong, T. Mohamed, and D. J. Han, “A Michelson interferometer for relative phase locking of optical beams,” J. Phys. Soc. Japan 77, 024301 (2008).

Li, J.

Liu, H.-K.

D. A. Gregory, J. A. Loudin, and H.-K. Liu, “Joint transform correlator limitations,” Proc. SPIE1053, 198–207 (1989).

Loudin, J. A.

D. A. Gregory, J. A. Loudin, and H.-K. Liu, “Joint transform correlator limitations,” Proc. SPIE1053, 198–207 (1989).

Lu, M.

M. Lu, H. C. Park, E. Bloch, L. A. Johansson, M. J. Rodwell, and L. A. Coldren, “An integrated heterodyne optical phase-locked loop with record offset locking frequency,” in Optical Fiber Communication Conference OSA Technical Digest Series (Optical Society of America, 2014), paper Tu2H.4.

Lu, X. J.

F. T. S. Yu and X. J. Lu, “A real-time programmable joint transform correlator,” Opt. Commun. 52(1), 10–16 (1984).
[Crossref]

Mendlovic, D.

D. Sazbon, Z. Zalevsky, E. Rivlin, and D. Mendlovic, “Using Fourier/Mellin-based correlators and their fractional versions in navigational tasks,” Pattern Recognit. 35(12), 2993–2999 (2002).
[Crossref]

Mohamed, T.

G. W. Li, S. J. Huang, H. S. Wu, S. Fang, D. S. Hong, T. Mohamed, and D. J. Han, “A Michelson interferometer for relative phase locking of optical beams,” J. Phys. Soc. Japan 77, 024301 (2008).

Monjur, M. S.

Noskov, M.

M. Noskov, V. Tutatchikov, M. Lapchik, M. Ragulina, and T. Yamskikh, “Application of parallel version two-dimensional fast Fourier transform algorithm, analog of the Cooley-Tukey algorithm, for digital image processing of satellite data,” in E3S Web of Conferences (EDP Sciences, 2019), paper 01012.

Park, H. C.

M. Lu, H. C. Park, E. Bloch, L. A. Johansson, M. J. Rodwell, and L. A. Coldren, “An integrated heterodyne optical phase-locked loop with record offset locking frequency,” in Optical Fiber Communication Conference OSA Technical Digest Series (Optical Society of America, 2014), paper Tu2H.4.

Pati, G. S.

Phan, C.

Psaltis, D.

D. Casasent and D. Psaltis, “New optical transforms for pattern recognition,” Proc. IEEE 65(1), 77–84 (1977).
[Crossref]

D. Casasent and D. Psaltis, “Scale invariant optical correlation using Mellin transforms,” Opt. Commun. 17(1), 59–63 (1976).
[Crossref]

D. Casasent and D. Psaltis, “Position, rotation, and scale invariant optical correlation,” Appl. Opt. 15(7), 1795–1799 (1976).
[Crossref] [PubMed]

Ragulina, M.

M. Noskov, V. Tutatchikov, M. Lapchik, M. Ragulina, and T. Yamskikh, “Application of parallel version two-dimensional fast Fourier transform algorithm, analog of the Cooley-Tukey algorithm, for digital image processing of satellite data,” in E3S Web of Conferences (EDP Sciences, 2019), paper 01012.

Rivlin, E.

D. Sazbon, Z. Zalevsky, E. Rivlin, and D. Mendlovic, “Using Fourier/Mellin-based correlators and their fractional versions in navigational tasks,” Pattern Recognit. 35(12), 2993–2999 (2002).
[Crossref]

Rodwell, M. J.

M. Lu, H. C. Park, E. Bloch, L. A. Johansson, M. J. Rodwell, and L. A. Coldren, “An integrated heterodyne optical phase-locked loop with record offset locking frequency,” in Optical Fiber Communication Conference OSA Technical Digest Series (Optical Society of America, 2014), paper Tu2H.4.

Rueckert, D.

W. Shi, J. Caballero, F. Huszár, J. Totz, A. Aitken, R. Bishop, D. Rueckert, and Z. Wang, “Real-Time Single Image and Video Super-Resolution Using an Efficient Sub-Pixel Convolutional Neural Network,” in IEEE Conference on Computer Vision and Pattern Recognition (CVPR) (2016), 1874–1883.
[Crossref]

Sazbon, D.

D. Sazbon, Z. Zalevsky, E. Rivlin, and D. Mendlovic, “Using Fourier/Mellin-based correlators and their fractional versions in navigational tasks,” Pattern Recognit. 35(12), 2993–2999 (2002).
[Crossref]

Shahriar, M. S.

Shahriar, S. M.

Shen, J. T.

Shi, W.

W. Shi, J. Caballero, F. Huszár, J. Totz, A. Aitken, R. Bishop, D. Rueckert, and Z. Wang, “Real-Time Single Image and Video Super-Resolution Using an Efficient Sub-Pixel Convolutional Neural Network,” in IEEE Conference on Computer Vision and Pattern Recognition (CVPR) (2016), 1874–1883.
[Crossref]

Shiau, B. W.

B. W. Shiau, T. P. Ku, and D. J. Han, “Real-time phase difference control of optical beams using a mach-zehnder interferometer,” J. Phys. Soc. Japan 79, 034302 (2010).

Tang, Q.

Totz, J.

W. Shi, J. Caballero, F. Huszár, J. Totz, A. Aitken, R. Bishop, D. Rueckert, and Z. Wang, “Real-Time Single Image and Video Super-Resolution Using an Efficient Sub-Pixel Convolutional Neural Network,” in IEEE Conference on Computer Vision and Pattern Recognition (CVPR) (2016), 1874–1883.
[Crossref]

Tripathi, R.

Tseng, S.

Tutatchikov, V.

M. Noskov, V. Tutatchikov, M. Lapchik, M. Ragulina, and T. Yamskikh, “Application of parallel version two-dimensional fast Fourier transform algorithm, analog of the Cooley-Tukey algorithm, for digital image processing of satellite data,” in E3S Web of Conferences (EDP Sciences, 2019), paper 01012.

Vander Lugt, A.

A. Vander Lugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory 10(2), 139–145 (1964).
[Crossref]

Wang, Z.

W. Shi, J. Caballero, F. Huszár, J. Totz, A. Aitken, R. Bishop, D. Rueckert, and Z. Wang, “Real-Time Single Image and Video Super-Resolution Using an Efficient Sub-Pixel Convolutional Neural Network,” in IEEE Conference on Computer Vision and Pattern Recognition (CVPR) (2016), 1874–1883.
[Crossref]

Weathers, W.

Woods, C.

Wu, H. S.

G. W. Li, S. J. Huang, H. S. Wu, S. Fang, D. S. Hong, T. Mohamed, and D. J. Han, “A Michelson interferometer for relative phase locking of optical beams,” J. Phys. Soc. Japan 77, 024301 (2008).

Yamamoto, M.

Yamskikh, T.

M. Noskov, V. Tutatchikov, M. Lapchik, M. Ragulina, and T. Yamskikh, “Application of parallel version two-dimensional fast Fourier transform algorithm, analog of the Cooley-Tukey algorithm, for digital image processing of satellite data,” in E3S Web of Conferences (EDP Sciences, 2019), paper 01012.

Yatagai, T.

Yu, F. T. S.

F. T. S. Yu and X. J. Lu, “A real-time programmable joint transform correlator,” Opt. Commun. 52(1), 10–16 (1984).
[Crossref]

Zalevsky, Z.

D. Sazbon, Z. Zalevsky, E. Rivlin, and D. Mendlovic, “Using Fourier/Mellin-based correlators and their fractional versions in navigational tasks,” Pattern Recognit. 35(12), 2993–2999 (2002).
[Crossref]

Appl. Opt. (7)

IEEE Trans. Inf. Theory (1)

A. Vander Lugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory 10(2), 139–145 (1964).
[Crossref]

J. Opt. Soc. Am. A (2)

J. Opt. Soc. Am. B (1)

J. Phys. Soc. Japan (2)

G. W. Li, S. J. Huang, H. S. Wu, S. Fang, D. S. Hong, T. Mohamed, and D. J. Han, “A Michelson interferometer for relative phase locking of optical beams,” J. Phys. Soc. Japan 77, 024301 (2008).

B. W. Shiau, T. P. Ku, and D. J. Han, “Real-time phase difference control of optical beams using a mach-zehnder interferometer,” J. Phys. Soc. Japan 79, 034302 (2010).

Opt. Commun. (3)

F. T. S. Yu and X. J. Lu, “A real-time programmable joint transform correlator,” Opt. Commun. 52(1), 10–16 (1984).
[Crossref]

D. Asselin and H. H. Arsenault, “Rotation and scale invariance with polar and log-polar coordinate transformations,” Opt. Commun. 104(4-6), 391–404 (1994).
[Crossref]

D. Casasent and D. Psaltis, “Scale invariant optical correlation using Mellin transforms,” Opt. Commun. 17(1), 59–63 (1976).
[Crossref]

Opt. Eng. (1)

A. Heifetz, J. T. Shen, J.-K. Lee, and M. S. Shahriar, “Translation-invariant object recognition system using an optical correlator and a super-parallel holographic random access memory,” Opt. Eng. 45, 025201 (2006).

Opt. Lett. (1)

Pattern Recognit. (1)

D. Sazbon, Z. Zalevsky, E. Rivlin, and D. Mendlovic, “Using Fourier/Mellin-based correlators and their fractional versions in navigational tasks,” Pattern Recognit. 35(12), 2993–2999 (2002).
[Crossref]

Proc. IEEE (1)

D. Casasent and D. Psaltis, “New optical transforms for pattern recognition,” Proc. IEEE 65(1), 77–84 (1977).
[Crossref]

Other (5)

D. A. Gregory, J. A. Loudin, and H.-K. Liu, “Joint transform correlator limitations,” Proc. SPIE1053, 198–207 (1989).

M. Lu, H. C. Park, E. Bloch, L. A. Johansson, M. J. Rodwell, and L. A. Coldren, “An integrated heterodyne optical phase-locked loop with record offset locking frequency,” in Optical Fiber Communication Conference OSA Technical Digest Series (Optical Society of America, 2014), paper Tu2H.4.

Because the PZT is an electro-mechanical device, it requires a voltage source and a control circuit that introduce electrical noise into the system. A PID controller allows the PZT to maintain a more stable position. However, PID systems require a feedback loop. An MZI was constructed to provide the feedback for the PID via interferometry. This constitutes a mechanically controlled OPLL. This would not be required in an integrated system where the functionality of the PZT may be replaced by other means of phase control.

W. Shi, J. Caballero, F. Huszár, J. Totz, A. Aitken, R. Bishop, D. Rueckert, and Z. Wang, “Real-Time Single Image and Video Super-Resolution Using an Efficient Sub-Pixel Convolutional Neural Network,” in IEEE Conference on Computer Vision and Pattern Recognition (CVPR) (2016), 1874–1883.
[Crossref]

M. Noskov, V. Tutatchikov, M. Lapchik, M. Ragulina, and T. Yamskikh, “Application of parallel version two-dimensional fast Fourier transform algorithm, analog of the Cooley-Tukey algorithm, for digital image processing of satellite data,” in E3S Web of Conferences (EDP Sciences, 2019), paper 01012.

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Figures (6)

Fig. 1
Fig. 1 Simplified architecture of the HOC for demonstrating the working principle using the PMT, shutters, and SLM’s.
Fig. 2
Fig. 2 Simplified HOC diagram. The numbers represent vertices used to describe path lengths.
Fig. 3
Fig. 3 PMT ASIC design and incorporation into the query arm of the simplified HOC architecture.
Fig. 4
Fig. 4 HOC results without the PMT. (A): Reference Input. (B): Query Input. (C): Measured FT of A. (D): Measured FT of B. (E): Output scaled to the intensity of a known match.
Fig. 5
Fig. 5 HOC results with the PMT. (A): Reference PMT Input (converted from 4.C). (B): Query PMT Input (converted from 4.D). (C): Detected FT of A. (D): Detected FT of B. (E): Output scaled to the intensity of a known match.
Fig. 6
Fig. 6 HOC simulation with the PMT. All images are simulated. (A): Reference PMT Input (from 4.A). (B): Query PMT Input (from 4.D). (C): 2-D Fast Fourier Transform (FFT) of A. (D): FFT of B. (E): Output normalized to 1.

Equations (21)

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M j =| M j |exp(i ϕ j ) C j =| C j |exp(i Ψ j )
  A j = | M j + C j | 2 = | M j | 2 + | C j | 2 +| M j | | C j | ( exp( i[ ϕ j Ψ j ] )+exp( i[ ϕ j Ψ j ] ) )
S j = A j B j C j =| M j | | C j |( exp( i[ ϕ j Ψ j ] )+exp( i[ ϕ j Ψ j ] ) ) = M j C j * + M j * C j
S= S 1 × S 2 =( M 1 C 1 * + M 1 * C 1 )×( M 2 C 2 * + M 2 * C 2 ) = α * M 1 M 2 + α M 1 * M 2 * + β * M 1 M 2 * + β M 1 * M 2
S f =F{ S } =  α * F{ M 1 M 2 }+ αF{ M 1 * M 2 * }+ β * F{ M 1 M 2 * }+ βF{ M 1 * M 2 }
S f = α * T 1 + α T 2 + β * T 3 + β T 4 T 1 = H 1 ( x,y ) H 2 ( x,y ) T 2 = H 1 ( x,y ) H 2 ( x,y ) T 3 = H 2 ( x,y ) H 1 ( x,y ) T 4 = H 1 ( x,y ) H 2 ( x,y )
α= C 1 C 2               β= C 1 C 2 * α=| C 1 || C 2 |exp( i( Ψ 1 + Ψ 2 ) )
β=| C 1 || C 2 |exp( i( Ψ 1 Ψ 2 ) )
L c1 = l 1,2 + l 2,3 + l 3,4 + l 4,5 + l 5,6 + l 6,7
L c2 = l 1,2 + l 2,3 + l 3,4 + l 4,8 + l 8,9 + l 9,10 + l 10,11
Ψ j =k× L cj ;    k=2π/λ
ΔΨ= Ψ 1 Ψ 2 =k×( L c1 L c2 )+Δ ϕ OE =k×[ l 4,5 + l 5,6 + l 6,7 ( l 4,8 + l 8,9 + l 9,10 + l 10,11 ) ]+Δ ϕ OE
ΣΨ= Ψ 1 + Ψ 2 =k×( L c1 + L c2 )+2 ϕ init =k×[ 2*( l 1,2 + l 2,3 + l 3,4 )+ l 4,5 + l 5,6 + l 6,7 + l 4,8 + l 8,9 + l 9,10 + l 10,11 ]+2 ϕ init
l 4,8 + l 8,9 =l ' 4,8 +l ' 8,9 +Δ l pzt l 4,5 + l 5,6 =l ' 4,5 +l ' 5,6 +Δ l ref
ΔΨ= k×[ l ' 4,5 +l ' 5,6 + l 6,7 ( l ' 4,8 +l ' 8,9 + l 9,10 + l 10,11 )+( Δ l ref Δ l pzt ) ]+Δ ϕ OE ΣΨ=k×[ 2*( l 1,2 + l 2,3 + l 3,4 )+l ' 4,5 +l ' 5,6 + l 6,7 +l ' 4,8 +l ' 8,9 + l 9,10 + l 10,11 +( Δ l ref l pzt ) ]+2 ϕ init
Δ l ref =Δ l pzt
ΔΨ= k×[ l ' 4,5 +l ' 5,6 + l 6,7 ( l ' 4,8 +l ' 8,9 + l 9,10 + l 10,11 )( l pzt ) ]+Δ ϕ OE ΣΨ=k×[ 2*( l 1,2 + l 2,3 + l 3,4 )+l ' 4,5 +l ' 5,6 + l 6,7 +l ' 4,8 +l ' 8,9 + l 9,10 + l 10,11 ]+2 ϕ init
ΔΨ MZI = Ψ control Ψ static
Ψ control =k×( l 3,4 +l ' 4,8 +l ' 8,9 + l 9,13 +Δ l pzt ) Ψ static =k×( l 3,12 + l 12,13 )
ΔΨ MZI =k×[ l 3,4 +l ' 4,8 +l ' 8,9 + l 9,13 +Δ l pzt ( l 3,12 + l 12,13 ) ]
S f = β * T 3 + β T 4 = β *  [ H 2 ( x,y ) H 1 ( x,y ) ]+β [ H 1 ( x,y ) H 2 ( x,y ) ]

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