Abstract

We describe the use of optical memory disks as elements in optical information processing architectures. The optical disk is an optical memory device with a storage capacity approaching 1010 bits which is naturally suited to parallel access. We discuss optical disk characteristics which are important in optical computing systems such as contrast, diffraction efficiency, and phase uniformity. We describe techniques for holographic storage on optical disks and present reconstructions of several types of computer-generated holograms. Various optical information processing architectures are described for applications such as database retrieval, neural network implementation, and image correlation. Selected systems are experimentally demonstrated.

© 1990 Optical Society of America

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References

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  1. R. Bartolini, H. Weakliem, B. Williams, “Review and Analysis of Optical Recording Media,” Opt. Eng. 15, 99–108 (1976).
    [CrossRef]
  2. Y. Abu-Mostafa, D. Psaltis, “Optical Neural Computers,” Sci. Am. 255, 88–95 (1987).
    [CrossRef]
  3. D. Psaltis, A. A. Yamamura, M. A. Neifeld, S. Kobayashi, “Parallel Readout of Optical Disks,” in Technical Digest, Topical Meeting on Optical Computing (Optical Society of America, Washington, DC, 1989), pp. 58–61.
  4. L. Giles, B. K. Jenkins, “Models of Parallel Computation and Optical Computing,” in Technical Digest, OSA Annual Meeting (Optical Society of America, Washington, DC, 1986), paper ML1.
  5. Y. Nakane et al., “Principle of Laser Recording Mechanism by Forming an Alloy in the Multilayer of Thin Metallic Films,” Proc. Soc. Photo-Opt. Instrum. Eng. 529, 76–81 (1985).
  6. D. Psaltis, E. G. Paek, S. S. Venkatesh, “Optical Image Correlation with a Binary Spatial Light Modulator,” Opt. Eng. 23, 698–704 (1984).
    [CrossRef]
  7. J. H. Rilum, A. R. Tanguay, “Utilization of Optical Memory Disks for Optical Information Processing,” in Technical Digest, OSA Annual Meeting (Optical Society of America, Washington, DC, 1988), paper M15.
  8. J. F. Jarvis, C. N. Judice, W. H. Ninke, “A Survey of Techniques for the Display of Continuous Tone Pictures on Bilevel Displays,” Comput. Graphics Image Process. 5, 13–40 (1976).
    [CrossRef]
  9. Y. Tsunoda, K. Tatsuno, K. Kataoka, Y. Takeda, “Holographic Video Disk: An Alternative Approach to Optical Video Disks,” Appl. Opt. 15, 1398–1403 (1976).
    [CrossRef] [PubMed]
  10. I. Satoh, M. Kato, “Holographic Disk Recording of Digital Data with Fringe Stabilization,” Appl. Opt. 27, 2987–2992 (1988).
    [CrossRef] [PubMed]
  11. T. Yatagai, J. G. Camacho-Basilio, H. Onda, “Recording of Computer-Generated Holograms on an Optical Disk Master,” Proc. Soc. Photo-Opt. Instrum. Eng. 1052, 119–124 (1989).
  12. T. Inagaki, “Hologram Lenses Lead to Compact Scanners,” IEEE Spectrum 26, 39–43 (1989).
    [CrossRef]
  13. B. Brown, A. Lohmann, “Complex Spatial Filtering with Binary Masks,” Appl. Opt. 5, 967–969 (1966).
    [CrossRef] [PubMed]
  14. W.-H. Lee, “Binary Computer Generated Holograms,” Appl. Opt. 18, 3661–3669 (1979).
    [CrossRef] [PubMed]
  15. G. Tricoles, “Computer Generated Holograms: An Historical Review,” Appl. Opt. 26, 4351–4360 (1987).
    [CrossRef] [PubMed]
  16. A. Lohmann, U. Erlangen-Nuremburg; personal communication.
  17. J. Alspector, R. B. Allen, “A Neuromorphic VLSI Learning System,” Advanced Research in VLSI Processes 1987 Stanford Research Conference (MIT Press, Cambridge, 1987), pp. 313–349.
  18. Special Issue on Neural Networks, Applied Optics 26, (1Dec.1987).
  19. J. H. Kim, S. H. Lin, J. Katz, D. Psaltis, “Monolithically Integrated 2-D Arrays of Optoelectronic Devices for Neural Network Applications,” Proc. Soc. Photo-Opt. Instrum. Eng. 1043, 44–52 (1989).
  20. A. VanderLugt, “Signal Detection by Complex Spatial Filtering,” IEEE Trans. Inf. Theory IT-10, 139 (1964).
    [CrossRef]
  21. D. Psaltis, M. A. Neifeld, A. A. Yamamura, “Optical Disk Based Correlation Architectures,” in Technical Digest, Topical Meeting on Optical Computing (Optical Society of America, Washington, DC, 1989), pp. 206–209.
  22. D. Psaltis, M. A. Neifeld, A. A. Yamamura, “Image Correlators Using Optical Memory Disks,” Opt. Lett. 14, 429–431 (1989).
    [CrossRef] [PubMed]
  23. J. Yu, “Optical Processing Using Photorefractive Crystals,” Ph.D. Thesis, California Institute of Technology (1988), Chap. 5.
  24. D. Psaltis, “Incoherent Electrooptic Image Correlator,” Opt. Eng. 23, 12–15 (1984).
  25. A. D. Mikaelyan, A. Vanin, E. D. Gulanyan, S. Prokopenko, “Holographic Disk for Data Storage,” Sov. J. Quantum Electronics. 170(5), 680–687 (1987).
    [CrossRef]

1989

T. Yatagai, J. G. Camacho-Basilio, H. Onda, “Recording of Computer-Generated Holograms on an Optical Disk Master,” Proc. Soc. Photo-Opt. Instrum. Eng. 1052, 119–124 (1989).

T. Inagaki, “Hologram Lenses Lead to Compact Scanners,” IEEE Spectrum 26, 39–43 (1989).
[CrossRef]

J. H. Kim, S. H. Lin, J. Katz, D. Psaltis, “Monolithically Integrated 2-D Arrays of Optoelectronic Devices for Neural Network Applications,” Proc. Soc. Photo-Opt. Instrum. Eng. 1043, 44–52 (1989).

D. Psaltis, M. A. Neifeld, A. A. Yamamura, “Image Correlators Using Optical Memory Disks,” Opt. Lett. 14, 429–431 (1989).
[CrossRef] [PubMed]

1988

1987

Y. Abu-Mostafa, D. Psaltis, “Optical Neural Computers,” Sci. Am. 255, 88–95 (1987).
[CrossRef]

A. D. Mikaelyan, A. Vanin, E. D. Gulanyan, S. Prokopenko, “Holographic Disk for Data Storage,” Sov. J. Quantum Electronics. 170(5), 680–687 (1987).
[CrossRef]

G. Tricoles, “Computer Generated Holograms: An Historical Review,” Appl. Opt. 26, 4351–4360 (1987).
[CrossRef] [PubMed]

Special Issue on Neural Networks, Applied Optics 26, (1Dec.1987).

1985

Y. Nakane et al., “Principle of Laser Recording Mechanism by Forming an Alloy in the Multilayer of Thin Metallic Films,” Proc. Soc. Photo-Opt. Instrum. Eng. 529, 76–81 (1985).

1984

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

D. Psaltis, “Incoherent Electrooptic Image Correlator,” Opt. Eng. 23, 12–15 (1984).

1979

1976

J. F. Jarvis, C. N. Judice, W. H. Ninke, “A Survey of Techniques for the Display of Continuous Tone Pictures on Bilevel Displays,” Comput. Graphics Image Process. 5, 13–40 (1976).
[CrossRef]

Y. Tsunoda, K. Tatsuno, K. Kataoka, Y. Takeda, “Holographic Video Disk: An Alternative Approach to Optical Video Disks,” Appl. Opt. 15, 1398–1403 (1976).
[CrossRef] [PubMed]

R. Bartolini, H. Weakliem, B. Williams, “Review and Analysis of Optical Recording Media,” Opt. Eng. 15, 99–108 (1976).
[CrossRef]

1966

1964

A. VanderLugt, “Signal Detection by Complex Spatial Filtering,” IEEE Trans. Inf. Theory IT-10, 139 (1964).
[CrossRef]

Abu-Mostafa, Y.

Y. Abu-Mostafa, D. Psaltis, “Optical Neural Computers,” Sci. Am. 255, 88–95 (1987).
[CrossRef]

Allen, R. B.

J. Alspector, R. B. Allen, “A Neuromorphic VLSI Learning System,” Advanced Research in VLSI Processes 1987 Stanford Research Conference (MIT Press, Cambridge, 1987), pp. 313–349.

Alspector, J.

J. Alspector, R. B. Allen, “A Neuromorphic VLSI Learning System,” Advanced Research in VLSI Processes 1987 Stanford Research Conference (MIT Press, Cambridge, 1987), pp. 313–349.

Bartolini, R.

R. Bartolini, H. Weakliem, B. Williams, “Review and Analysis of Optical Recording Media,” Opt. Eng. 15, 99–108 (1976).
[CrossRef]

Brown, B.

Camacho-Basilio, J. G.

T. Yatagai, J. G. Camacho-Basilio, H. Onda, “Recording of Computer-Generated Holograms on an Optical Disk Master,” Proc. Soc. Photo-Opt. Instrum. Eng. 1052, 119–124 (1989).

Giles, L.

L. Giles, B. K. Jenkins, “Models of Parallel Computation and Optical Computing,” in Technical Digest, OSA Annual Meeting (Optical Society of America, Washington, DC, 1986), paper ML1.

Gulanyan, E. D.

A. D. Mikaelyan, A. Vanin, E. D. Gulanyan, S. Prokopenko, “Holographic Disk for Data Storage,” Sov. J. Quantum Electronics. 170(5), 680–687 (1987).
[CrossRef]

Inagaki, T.

T. Inagaki, “Hologram Lenses Lead to Compact Scanners,” IEEE Spectrum 26, 39–43 (1989).
[CrossRef]

Jarvis, J. F.

J. F. Jarvis, C. N. Judice, W. H. Ninke, “A Survey of Techniques for the Display of Continuous Tone Pictures on Bilevel Displays,” Comput. Graphics Image Process. 5, 13–40 (1976).
[CrossRef]

Jenkins, B. K.

L. Giles, B. K. Jenkins, “Models of Parallel Computation and Optical Computing,” in Technical Digest, OSA Annual Meeting (Optical Society of America, Washington, DC, 1986), paper ML1.

Judice, C. N.

J. F. Jarvis, C. N. Judice, W. H. Ninke, “A Survey of Techniques for the Display of Continuous Tone Pictures on Bilevel Displays,” Comput. Graphics Image Process. 5, 13–40 (1976).
[CrossRef]

Kataoka, K.

Kato, M.

Katz, J.

J. H. Kim, S. H. Lin, J. Katz, D. Psaltis, “Monolithically Integrated 2-D Arrays of Optoelectronic Devices for Neural Network Applications,” Proc. Soc. Photo-Opt. Instrum. Eng. 1043, 44–52 (1989).

Kim, J. H.

J. H. Kim, S. H. Lin, J. Katz, D. Psaltis, “Monolithically Integrated 2-D Arrays of Optoelectronic Devices for Neural Network Applications,” Proc. Soc. Photo-Opt. Instrum. Eng. 1043, 44–52 (1989).

Kobayashi, S.

D. Psaltis, A. A. Yamamura, M. A. Neifeld, S. Kobayashi, “Parallel Readout of Optical Disks,” in Technical Digest, Topical Meeting on Optical Computing (Optical Society of America, Washington, DC, 1989), pp. 58–61.

Lee, W.-H.

Lin, S. H.

J. H. Kim, S. H. Lin, J. Katz, D. Psaltis, “Monolithically Integrated 2-D Arrays of Optoelectronic Devices for Neural Network Applications,” Proc. Soc. Photo-Opt. Instrum. Eng. 1043, 44–52 (1989).

Lohmann, A.

Mikaelyan, A. D.

A. D. Mikaelyan, A. Vanin, E. D. Gulanyan, S. Prokopenko, “Holographic Disk for Data Storage,” Sov. J. Quantum Electronics. 170(5), 680–687 (1987).
[CrossRef]

Nakane, Y.

Y. Nakane et al., “Principle of Laser Recording Mechanism by Forming an Alloy in the Multilayer of Thin Metallic Films,” Proc. Soc. Photo-Opt. Instrum. Eng. 529, 76–81 (1985).

Neifeld, M. A.

D. Psaltis, M. A. Neifeld, A. A. Yamamura, “Image Correlators Using Optical Memory Disks,” Opt. Lett. 14, 429–431 (1989).
[CrossRef] [PubMed]

D. Psaltis, M. A. Neifeld, A. A. Yamamura, “Optical Disk Based Correlation Architectures,” in Technical Digest, Topical Meeting on Optical Computing (Optical Society of America, Washington, DC, 1989), pp. 206–209.

D. Psaltis, A. A. Yamamura, M. A. Neifeld, S. Kobayashi, “Parallel Readout of Optical Disks,” in Technical Digest, Topical Meeting on Optical Computing (Optical Society of America, Washington, DC, 1989), pp. 58–61.

Ninke, W. H.

J. F. Jarvis, C. N. Judice, W. H. Ninke, “A Survey of Techniques for the Display of Continuous Tone Pictures on Bilevel Displays,” Comput. Graphics Image Process. 5, 13–40 (1976).
[CrossRef]

Onda, H.

T. Yatagai, J. G. Camacho-Basilio, H. Onda, “Recording of Computer-Generated Holograms on an Optical Disk Master,” Proc. Soc. Photo-Opt. Instrum. Eng. 1052, 119–124 (1989).

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]

Prokopenko, S.

A. D. Mikaelyan, A. Vanin, E. D. Gulanyan, S. Prokopenko, “Holographic Disk for Data Storage,” Sov. J. Quantum Electronics. 170(5), 680–687 (1987).
[CrossRef]

Psaltis, D.

D. Psaltis, M. A. Neifeld, A. A. Yamamura, “Image Correlators Using Optical Memory Disks,” Opt. Lett. 14, 429–431 (1989).
[CrossRef] [PubMed]

J. H. Kim, S. H. Lin, J. Katz, D. Psaltis, “Monolithically Integrated 2-D Arrays of Optoelectronic Devices for Neural Network Applications,” Proc. Soc. Photo-Opt. Instrum. Eng. 1043, 44–52 (1989).

Y. Abu-Mostafa, D. Psaltis, “Optical Neural Computers,” Sci. Am. 255, 88–95 (1987).
[CrossRef]

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

D. Psaltis, “Incoherent Electrooptic Image Correlator,” Opt. Eng. 23, 12–15 (1984).

D. Psaltis, M. A. Neifeld, A. A. Yamamura, “Optical Disk Based Correlation Architectures,” in Technical Digest, Topical Meeting on Optical Computing (Optical Society of America, Washington, DC, 1989), pp. 206–209.

D. Psaltis, A. A. Yamamura, M. A. Neifeld, S. Kobayashi, “Parallel Readout of Optical Disks,” in Technical Digest, Topical Meeting on Optical Computing (Optical Society of America, Washington, DC, 1989), pp. 58–61.

Rilum, J. H.

J. H. Rilum, A. R. Tanguay, “Utilization of Optical Memory Disks for Optical Information Processing,” in Technical Digest, OSA Annual Meeting (Optical Society of America, Washington, DC, 1988), paper M15.

Satoh, I.

Takeda, Y.

Tanguay, A. R.

J. H. Rilum, A. R. Tanguay, “Utilization of Optical Memory Disks for Optical Information Processing,” in Technical Digest, OSA Annual Meeting (Optical Society of America, Washington, DC, 1988), paper M15.

Tatsuno, K.

Tricoles, G.

Tsunoda, Y.

VanderLugt, A.

A. VanderLugt, “Signal Detection by Complex Spatial Filtering,” IEEE Trans. Inf. Theory IT-10, 139 (1964).
[CrossRef]

Vanin, A.

A. D. Mikaelyan, A. Vanin, E. D. Gulanyan, S. Prokopenko, “Holographic Disk for Data Storage,” Sov. J. Quantum Electronics. 170(5), 680–687 (1987).
[CrossRef]

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]

Weakliem, H.

R. Bartolini, H. Weakliem, B. Williams, “Review and Analysis of Optical Recording Media,” Opt. Eng. 15, 99–108 (1976).
[CrossRef]

Williams, B.

R. Bartolini, H. Weakliem, B. Williams, “Review and Analysis of Optical Recording Media,” Opt. Eng. 15, 99–108 (1976).
[CrossRef]

Yamamura, A. A.

D. Psaltis, M. A. Neifeld, A. A. Yamamura, “Image Correlators Using Optical Memory Disks,” Opt. Lett. 14, 429–431 (1989).
[CrossRef] [PubMed]

D. Psaltis, M. A. Neifeld, A. A. Yamamura, “Optical Disk Based Correlation Architectures,” in Technical Digest, Topical Meeting on Optical Computing (Optical Society of America, Washington, DC, 1989), pp. 206–209.

D. Psaltis, A. A. Yamamura, M. A. Neifeld, S. Kobayashi, “Parallel Readout of Optical Disks,” in Technical Digest, Topical Meeting on Optical Computing (Optical Society of America, Washington, DC, 1989), pp. 58–61.

Yatagai, T.

T. Yatagai, J. G. Camacho-Basilio, H. Onda, “Recording of Computer-Generated Holograms on an Optical Disk Master,” Proc. Soc. Photo-Opt. Instrum. Eng. 1052, 119–124 (1989).

Yu, J.

J. Yu, “Optical Processing Using Photorefractive Crystals,” Ph.D. Thesis, California Institute of Technology (1988), Chap. 5.

Appl. Opt.

Applied Optics

Special Issue on Neural Networks, Applied Optics 26, (1Dec.1987).

Comput. Graphics Image Process.

J. F. Jarvis, C. N. Judice, W. H. Ninke, “A Survey of Techniques for the Display of Continuous Tone Pictures on Bilevel Displays,” Comput. Graphics Image Process. 5, 13–40 (1976).
[CrossRef]

IEEE Spectrum

T. Inagaki, “Hologram Lenses Lead to Compact Scanners,” IEEE Spectrum 26, 39–43 (1989).
[CrossRef]

IEEE Trans. Inf. Theory

A. VanderLugt, “Signal Detection by Complex Spatial Filtering,” IEEE Trans. Inf. Theory IT-10, 139 (1964).
[CrossRef]

Opt. Eng.

D. Psaltis, “Incoherent Electrooptic Image Correlator,” Opt. Eng. 23, 12–15 (1984).

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

R. Bartolini, H. Weakliem, B. Williams, “Review and Analysis of Optical Recording Media,” Opt. Eng. 15, 99–108 (1976).
[CrossRef]

Opt. Lett.

Proc. Soc. Photo-Opt. Instrum. Eng.

Y. Nakane et al., “Principle of Laser Recording Mechanism by Forming an Alloy in the Multilayer of Thin Metallic Films,” Proc. Soc. Photo-Opt. Instrum. Eng. 529, 76–81 (1985).

J. H. Kim, S. H. Lin, J. Katz, D. Psaltis, “Monolithically Integrated 2-D Arrays of Optoelectronic Devices for Neural Network Applications,” Proc. Soc. Photo-Opt. Instrum. Eng. 1043, 44–52 (1989).

T. Yatagai, J. G. Camacho-Basilio, H. Onda, “Recording of Computer-Generated Holograms on an Optical Disk Master,” Proc. Soc. Photo-Opt. Instrum. Eng. 1052, 119–124 (1989).

Sci. Am.

Y. Abu-Mostafa, D. Psaltis, “Optical Neural Computers,” Sci. Am. 255, 88–95 (1987).
[CrossRef]

Sov. J. Quantum Electronics.

A. D. Mikaelyan, A. Vanin, E. D. Gulanyan, S. Prokopenko, “Holographic Disk for Data Storage,” Sov. J. Quantum Electronics. 170(5), 680–687 (1987).
[CrossRef]

Other

J. Yu, “Optical Processing Using Photorefractive Crystals,” Ph.D. Thesis, California Institute of Technology (1988), Chap. 5.

D. Psaltis, M. A. Neifeld, A. A. Yamamura, “Optical Disk Based Correlation Architectures,” in Technical Digest, Topical Meeting on Optical Computing (Optical Society of America, Washington, DC, 1989), pp. 206–209.

D. Psaltis, A. A. Yamamura, M. A. Neifeld, S. Kobayashi, “Parallel Readout of Optical Disks,” in Technical Digest, Topical Meeting on Optical Computing (Optical Society of America, Washington, DC, 1989), pp. 58–61.

L. Giles, B. K. Jenkins, “Models of Parallel Computation and Optical Computing,” in Technical Digest, OSA Annual Meeting (Optical Society of America, Washington, DC, 1986), paper ML1.

J. H. Rilum, A. R. Tanguay, “Utilization of Optical Memory Disks for Optical Information Processing,” in Technical Digest, OSA Annual Meeting (Optical Society of America, Washington, DC, 1988), paper M15.

A. Lohmann, U. Erlangen-Nuremburg; personal communication.

J. Alspector, R. B. Allen, “A Neuromorphic VLSI Learning System,” Advanced Research in VLSI Processes 1987 Stanford Research Conference (MIT Press, Cambridge, 1987), pp. 313–349.

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Figures (30)

Fig. 1
Fig. 1

Sony prototype optical disk system.

Fig. 2
Fig. 2

Sampled-format tracking and timing information system.

Fig. 3
Fig. 3

Far field diffraction pattern from grating: (a) grating written on inner tracks (R = 3 cm); and (b) grating written on outer tracks (R = 6 cm).

Fig. 4
Fig. 4

Interferogram of Sony WORM disk.

Fig. 5
Fig. 5

Coordinate system for calculating the effect of track curvature.

Fig. 6
Fig. 6

Photograph of image written on Sony WORM disk.

Fig. 7
Fig. 7

High contrast image obtained by imaging the first-order diffracted component of light reflected by the disk used in Fig. 1.

Fig. 8
Fig. 8

Grey scale image written on optical disk using area modulation.

Fig. 9
Fig. 9

Reconstruction of a binary Fresnel hologram stored on optical disk.

Fig. 10
Fig. 10

Reconstruction of Fresnel hologram stored on magnetooptic disk.

Fig. 11
Fig. 11

Schematic of CGH technique used to record complex valued pixels: (a) one-dimensional superpixel used to code phase information; and (b) complex values recordable using (a).

Fig. 12
Fig. 12

Reconstruction of Fourier transform hologram.

Fig. 13
Fig. 13

Reconstruction of Fourier along track/Fresnel across track hologram.

Fig. 14
Fig. 14

Multilayer feedforward neural network.

Fig. 15
Fig. 15

Optical disk/VLSI hybrid neural network implementation.

Fig. 16
Fig. 16

Schematic of VLSI neural network crossbar implementation.

Fig. 17
Fig. 17

Synapse circuit diagram.

Fig. 18
Fig. 18

Photograph of MDAC synapses.

Fig. 19
Fig. 19

Synapse current dependence on Vref.

Fig. 20
Fig. 20

Synaptic time response dependence on light intensity.

Fig. 21
Fig. 21

Optical disk implementation of synaptic connections.

Fig. 22
Fig. 22

Optical disk based VanderLugt correlator.

Fig. 23
Fig. 23

Photorefractive/optical disk based correlator.

Fig. 24
Fig. 24

Disk based Fourier plane correlator results using a plate: (a) input image recorded on disk 1 and used to record the hologram; (b) correlation pattern obtained using disk 2 as reference to read out the hologram.

Fig. 25
Fig. 25

Rotating mirror correlator.

Fig. 26
Fig. 26

Rotating mirror correlator results: (a) reference image recorded on Sony disk; (b) computer-generated autocorrelation signal; and (c) optical system output.

Fig. 27
Fig. 27

Moving AO lens correlator.

Fig. 28
Fig. 28

Impulse response of the AO lens scanner: (a) optical system used to measure impulse response; (b)–(d) image formed on CCD for various delay times Δ, where Δ is the time between the leftmost edge of the chirp gate (upper trace) and the laser diode trigger (lower trace), (b) Δ = 2.5 μs, (c) Δ = 5.0 μs, (d) Δ = 8.0 μs.

Fig. 29
Fig. 29

Output of AO lens correlator: (a) reference on disk; (b) optical system output; and (c) magnified version of (b) to resolve individual radial scan peaks.

Fig. 30
Fig. 30

Model of spot shapes.

Equations (42)

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

{ x = r sin ( θ ) y = r cos ( θ ) - R } .
{ Δ x = R δ θ Δ y = δ r } .
{ x = n Δ x y = m Δ y } ,
{ r = R + m δ r + n δ θ δ r 2 π θ = n δ θ } .
{ x = ( R + m δ r + n δ θ δ r 2 π ) sin ( n δ θ ) n δ x + n m Δ x Δ y R y = ( R + m δ r + n δ θ δ r 2 π ) cos ( n δ θ ) - R m Δ y + n Δ x Δ y 2 π R - n 2 Δ x 2 2 R } .
{ x = x - x n m Δ x Δ y R = x y R y = y - y n Δ x Δ y 2 π R - n 2 Δ x 2 2 R = x Δ y 2 π R - x 2 2 R } .
r ( x , y ) = r 0 + ( r 1 - r 0 ) [ n , m b n m δ ( x - n Δ x , y - m Δ y ) ] s ( x , y ) ,
E r ( x , y ) = E i ( x , y ) r ( x , y ) .
E ( x , y , z ) = E r ( x , y ) z exp ( j k l ) j λ l 2 d x d y .
l 2 = ( x - x ) 2 + ( y - y ) 2 + z 2 .
η = Σ E ( x , y , z ) 2 d x d y d z E i ( x , y ) 2 d x d y .
r ( x , y ) = r 0 + ( r 1 - r 0 ) [ b ( x , y ) n , m δ ( x - n Δ x , y - m Δ y ˙ ) ] s ( x , y ) ,
R ( u , v ) = r 0 δ ( u , v ) + ( r 1 - r 0 ) × [ B ( u , v ) 1 Δ x Δ y n , m δ ( u - n Δ x , v - m Δ y ) ] S ( u , v ) ,
R 1 ( u , v ) = r 1 - r 0 Δ x Δ y B ( u , v - 1 Δ y ) S ( u , v ) .
η = R 1 ( u , v ) 2 d u d v .
ϕ err ( x , y ; k ¯ ) = k ¯ · ( x , y ) = - k y x 2 2 R = k 2 f x 2 ,
f = - R k k y
k y = { 2 π Δ y for the + 1 order , - 2 π Δ y for the - 1 order .
E r ( x , y ) = E i ( x , y ) r ˜ ( x , y ) ,
h p ( x , y ) sgn [ Re { δ ( x - x 0 , y - y 0 ) × exp ( j π λ z 0 ) [ ( x - x ) 2 + ( y - y ) 2 ] d x d y } ] ,
sgn [ cos ( π λ z 0 [ ( x - x 0 ) 2 + ( y - y 0 ) 2 ] ) ] .
h ( x , y ) = sgn [ m cos ( π λ z m [ ( x - x m ) 2 + ( y - y m ) 2 ] ) ] ,
h ( x , y ) = b ( x , y ) exp [ j π λ z 0 ( y - y ) 2 ] exp ( - j 2 π λ z 0 x x ) d x d y .
{ δ x = λ F Δ x N x δ x = λ F Δ y N y }
{ x ( θ ) = λ F 2 Δ y [ cos ( θ ) - 1 ] y ( θ ) = λ F 2 Δ x sin ( θ ) } .
{ N x < λ F Δ x x ( θ ) N y < λ F Δ y y ( θ ) } .
{ N x < 4 Δ y / R 3 δ θ N x N y < 2 R Δ y } .
{ x j l = k w j k l y k l - 1 y j 1 = f ( x j 1 ) } ,
c ( x ˜ , y ˜ ) = F - 1 { F ( w x , w y ) G * ( w x , w y ) }
= f ( x , y ) g ( x - x ˜ , y - y ˜ ) d x d y ,
n p = τ P c / h ν ,
P c = η P s / 2.
t C = t AO ( S B P IN / S B P AO ) ,
i ( x , y ) = r 0 + ( r 1 - r 0 ) [ b ( x , y ) n , m δ ( x - n Δ x , y - m Δ y ) ] circ ( r Δ r ) + ( r 2 - 2 r 1 + r 0 ) n , m { [ b ( x , y ) δ ( x - n Δ x , y - m Δ y ) ] circ ( r Δ r ) } × { [ b ( x , y ) δ ( x - ( n + 1 ) Δ x , y - m Δ y ) ] circ ( r Δ r ) } ,
i ( x , y ) = r 0 + ( r 1 - r 0 ) [ b ( x , y ) n , m δ ( x - n Δ x , y - m Δ y ) ] [ circ ( r Δ r ) rect ( x Δ x ) ] .
I ( u , v ) = r 0 δ ( u , v ) + ( r 1 - r 0 ) [ B ( u , v ) 1 Δ x Δ y δ ( u - n Δ x , v - m Δ y ) ] × [ Δ r J 1 ( 2 π Δ r ρ ) ρ Δ x sinc ( Δ x u ) δ ( v ) ] ρ 2 = u 2 + v 2
H n m = | Δ r ( r 1 - r 0 ) Δ x Δ y | 2 - - | B ( u - n Δ x , v - m Δ y ) × [ J 1 ( 2 π Δ r ρ ) ρ Δ x sinc ( Δ x u ) δ ( v ) ] | 2 d u d v .
H n m | ( r 1 - r 0 ) Δ x Δ y | 2 - - | ( u - n Δ x , v - m Δ y ) | 2 d u d v × | Δ r J 1 ( 2 π Δ r ρ ) ρ Δ x sinc ( Δ x u ) δ ( v ) | u = n / Δ x , v = m / Δ y 2 .
H n m | ( r 1 - r 0 ) Δ x Δ y | 2 - - b ( x , y ) 2 d x d y × | Δ r J 1 ( 2 π Δ r ρ ) ρ Δ x sinc ( Δ x u ) δ ( v ) | u = n / Δ x , v = m / Δ y 2 .
H n m n , m = - H n , m = | Δ r J 1 ( 2 π Δ r ρ ) ρ Δ x sinc ( Δ x u ) δ ( v ) | u = n / Δ x , v = m / Δ y 2 n , m = - | Δ r J 1 ( 2 π Δ r ρ ) ρ Δ x sinc ( Δ x u ) δ ( v ) | u = n / Δ x , v = m / Δ y 2 .
H n m n , m = - H n , m = | Δ r J 1 ( 2 π Δ r ρ ) ρ Δ x sinc ( Δ x u ) δ ( v ) | u = n / Δ x , v = m / Δ y 2 1 Δ x Δ y - Δ x / 2 Δ x / 2 - Δ y / 2 Δ y / 2 | circ ( r Δ r ) rect ( x Δ x ) | 2 d x d y ,
= | Δ r J 1 ( 2 π Δ r ρ ) ρ Δ x sinc ( Δ x u ) δ ( v ) | u = n / Δ x , v = m / Δ y 2 1 Δ x Δ y [ 2 Δ r 2 Δ x Δ y sin - 1 ( Δ x 2 Δ r ) + Δ r Δ y 1 - Δ x 2 Δ r ] .

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