Abstract

A new approach to incoherent-to-coherent optical conversion based on a real-time five-wave-mixing technique in photoanisotropic organic film is presented. A uniform grating is written holographically in the sample and then erased locally by an incident white-light image. Subsequent coherent diffraction of the spatially modulated grating imposes the incoherent image upon the reading laser beam, permitting subsequent coherent optical processing. A theoretical analysis of the holographic recording and erasing mechanism in these photoanisotropic materials is presented, and the saturation is shown to be responsible for the grating intermodulation that produces the incoherent-to-coherent conversion. Experimental results of white-light images converted to inverted coherent images in real time are presented, and the resolution is shown to exceed 28 line pairs/mm.

© 1993 Optical Society of America

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References

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  1. A. R. Tanguay, “Materials requirements for optical processing and computing devices,” Opt. Eng. 24, 2–18 (1985).
  2. J. A. Neff, R. A. Athale, S. H. Lee, “Two-dimensional spatial light modulators: a tutorial,” Proc. IEEE 78, 826–855 (1990).
    [CrossRef]
  3. A. A. Kamshilin, M. P. Petrov, “Holographic image conversion in a Bi12SiO20,” Sov. Tech. Phys. Lett. 6, 144–145 (1980).
  4. H. J. Caulfield, W. T. Cathey, “Spatial light modulator and process of modulation,” U.S. Patent4,429,954 (7February1984).
  5. J. W. Yu, D. Psaltis, A. Marrakchi, A. R. Tanguay, R. V. Johnson, “The photorefractive incoherent-to-coherent optical converter,” in Photorefractive Materials and Their Applications II, P. Guinter, J. -P. Huignard, eds. (Springer-Verlag, New York, 1989), pp. 275–323.
    [CrossRef]
  6. T. Todorov, L. Nikolova, N. Tomova, “Polarization holography. 1: Anew high efficiency organic material with reversible photoinduced birefringence,” Appl. Opt. 23, 4309–4312 (1984).
    [CrossRef] [PubMed]
  7. J. J. A. Couture, R. A. Lessard, “Modulation transfer function measurements for thin layers of azo dyes in PVA matrix used as an optical recording material,” Appl. Opt. 27, 3368–3374 (1988).
    [CrossRef] [PubMed]
  8. H. Rajbenbach, “Digital optical processing with photorefractive materials: applications of a parallel half-adder circuit to algorithmic state machines,” J. Appl. Phys. 62, 4675–4681 (1987).
    [CrossRef]
  9. C. H. Wang, B. K. Jenkins, “Subtracting incoherent optical neuron model: analysis, experiment, and applications,” Appl. Opt. 29, 2171–2186 (1990).
    [CrossRef] [PubMed]
  10. A. M. Makushenko, B. S. Neporent, O. V. Stolbova, “Reversible orientational photodichroism and photoisomerization of aromatic azo compounds. I: Model of the system,” Opt. Spectrosc. (USSR) 31, 295–299 (1971).
  11. C. M. Verber, R. E. Schwerzel, P. J. Perry, R. A. Craig, “Holographic recording materials development,” NTIS Rep. N76–23544 (Battelle Memorial Laboratories, Columbus, Ohio, 1976).
  12. G. Smets, “Photochromic phenomena in the solid phase,” Adv. Polym. Sci. 50, 17–44 (1983).
    [CrossRef]
  13. L. Nikolova, P. Markovsky, N. Tomova, V. Dragostinova, N. Mateva, “Optically controlled photo-induced birefringence in photo-anisotropic materials,” J. Mod. Opt. 35, 1789–1799 (1988).
    [CrossRef]
  14. T. Tsutsui, A. Hatakeyama, S. Saito, “Analysis of thermal reactions of photochromic species in glassy matrices based on the concept of dispersive processes,” Chem. Phys. Lett. 132, 563–566 (1986).
    [CrossRef]
  15. K. Horie, I. Mita, “Reactions and photodynamics in polymer solids,” Adv. Polym. Sci. 88, 77–128 (1989).
    [CrossRef]
  16. R. Richert, “Analysis of non-exponential first-order reactions,” Chem. Phys. Lett. 118, 534–538 (1985).
    [CrossRef]
  17. R. Richert, H. Bässler, “Merocyanine ↔ spiropyran transformation in a polymer matrix: an example of a dispersive chemical reaction,” Chem. Phys. Lett. 116, 302–306 (1985).
    [CrossRef]
  18. Sh. D. Kakichashvili, “Polarization-holographic recording in the general case of a reaction of a photoanisotropic medium,” Sov. J. Quantum Electron. 13, 1317–1319 (1983).
    [CrossRef]
  19. Sh. D. Kakichashvili, “Regularity in photoanisotropic phenomena,” Opt. Spectrosc. (USSR) 52, 191–194 (1982).
  20. C. H. Kwak, J. T. Kim, S. S. Lee, “Scalar and vector holographic gratings recorded in a photoanisotropic amorphous As2S3 thin film,” Opt. Lett. 13, 437–439 (1988).
    [CrossRef] [PubMed]
  21. I. B. Joseph, Y. Silberberg, “Real time holography through triplet state absorption in organic dyes,” Opt. Commun. 41, 455–458 (1982).
    [CrossRef]
  22. H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).
  23. M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1987), pp. 548–549.
  24. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), pp. 110–120.
  25. R. Kingslake, Optical System Design (Academic, New York, 1983), pp. 269–272.

1990

J. A. Neff, R. A. Athale, S. H. Lee, “Two-dimensional spatial light modulators: a tutorial,” Proc. IEEE 78, 826–855 (1990).
[CrossRef]

C. H. Wang, B. K. Jenkins, “Subtracting incoherent optical neuron model: analysis, experiment, and applications,” Appl. Opt. 29, 2171–2186 (1990).
[CrossRef] [PubMed]

1989

K. Horie, I. Mita, “Reactions and photodynamics in polymer solids,” Adv. Polym. Sci. 88, 77–128 (1989).
[CrossRef]

1988

1987

H. Rajbenbach, “Digital optical processing with photorefractive materials: applications of a parallel half-adder circuit to algorithmic state machines,” J. Appl. Phys. 62, 4675–4681 (1987).
[CrossRef]

1986

T. Tsutsui, A. Hatakeyama, S. Saito, “Analysis of thermal reactions of photochromic species in glassy matrices based on the concept of dispersive processes,” Chem. Phys. Lett. 132, 563–566 (1986).
[CrossRef]

1985

R. Richert, “Analysis of non-exponential first-order reactions,” Chem. Phys. Lett. 118, 534–538 (1985).
[CrossRef]

R. Richert, H. Bässler, “Merocyanine ↔ spiropyran transformation in a polymer matrix: an example of a dispersive chemical reaction,” Chem. Phys. Lett. 116, 302–306 (1985).
[CrossRef]

A. R. Tanguay, “Materials requirements for optical processing and computing devices,” Opt. Eng. 24, 2–18 (1985).

1984

1983

Sh. D. Kakichashvili, “Polarization-holographic recording in the general case of a reaction of a photoanisotropic medium,” Sov. J. Quantum Electron. 13, 1317–1319 (1983).
[CrossRef]

G. Smets, “Photochromic phenomena in the solid phase,” Adv. Polym. Sci. 50, 17–44 (1983).
[CrossRef]

1982

Sh. D. Kakichashvili, “Regularity in photoanisotropic phenomena,” Opt. Spectrosc. (USSR) 52, 191–194 (1982).

I. B. Joseph, Y. Silberberg, “Real time holography through triplet state absorption in organic dyes,” Opt. Commun. 41, 455–458 (1982).
[CrossRef]

1980

A. A. Kamshilin, M. P. Petrov, “Holographic image conversion in a Bi12SiO20,” Sov. Tech. Phys. Lett. 6, 144–145 (1980).

1971

A. M. Makushenko, B. S. Neporent, O. V. Stolbova, “Reversible orientational photodichroism and photoisomerization of aromatic azo compounds. I: Model of the system,” Opt. Spectrosc. (USSR) 31, 295–299 (1971).

1969

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).

Athale, R. A.

J. A. Neff, R. A. Athale, S. H. Lee, “Two-dimensional spatial light modulators: a tutorial,” Proc. IEEE 78, 826–855 (1990).
[CrossRef]

Bässler, H.

R. Richert, H. Bässler, “Merocyanine ↔ spiropyran transformation in a polymer matrix: an example of a dispersive chemical reaction,” Chem. Phys. Lett. 116, 302–306 (1985).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1987), pp. 548–549.

Cathey, W. T.

H. J. Caulfield, W. T. Cathey, “Spatial light modulator and process of modulation,” U.S. Patent4,429,954 (7February1984).

Caulfield, H. J.

H. J. Caulfield, W. T. Cathey, “Spatial light modulator and process of modulation,” U.S. Patent4,429,954 (7February1984).

Couture, J. J. A.

Craig, R. A.

C. M. Verber, R. E. Schwerzel, P. J. Perry, R. A. Craig, “Holographic recording materials development,” NTIS Rep. N76–23544 (Battelle Memorial Laboratories, Columbus, Ohio, 1976).

Dragostinova, V.

L. Nikolova, P. Markovsky, N. Tomova, V. Dragostinova, N. Mateva, “Optically controlled photo-induced birefringence in photo-anisotropic materials,” J. Mod. Opt. 35, 1789–1799 (1988).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), pp. 110–120.

Hatakeyama, A.

T. Tsutsui, A. Hatakeyama, S. Saito, “Analysis of thermal reactions of photochromic species in glassy matrices based on the concept of dispersive processes,” Chem. Phys. Lett. 132, 563–566 (1986).
[CrossRef]

Horie, K.

K. Horie, I. Mita, “Reactions and photodynamics in polymer solids,” Adv. Polym. Sci. 88, 77–128 (1989).
[CrossRef]

Jenkins, B. K.

Johnson, R. V.

J. W. Yu, D. Psaltis, A. Marrakchi, A. R. Tanguay, R. V. Johnson, “The photorefractive incoherent-to-coherent optical converter,” in Photorefractive Materials and Their Applications II, P. Guinter, J. -P. Huignard, eds. (Springer-Verlag, New York, 1989), pp. 275–323.
[CrossRef]

Joseph, I. B.

I. B. Joseph, Y. Silberberg, “Real time holography through triplet state absorption in organic dyes,” Opt. Commun. 41, 455–458 (1982).
[CrossRef]

Kakichashvili, Sh. D.

Sh. D. Kakichashvili, “Polarization-holographic recording in the general case of a reaction of a photoanisotropic medium,” Sov. J. Quantum Electron. 13, 1317–1319 (1983).
[CrossRef]

Sh. D. Kakichashvili, “Regularity in photoanisotropic phenomena,” Opt. Spectrosc. (USSR) 52, 191–194 (1982).

Kamshilin, A. A.

A. A. Kamshilin, M. P. Petrov, “Holographic image conversion in a Bi12SiO20,” Sov. Tech. Phys. Lett. 6, 144–145 (1980).

Kim, J. T.

Kingslake, R.

R. Kingslake, Optical System Design (Academic, New York, 1983), pp. 269–272.

Kogelnik, H.

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).

Kwak, C. H.

Lee, S. H.

J. A. Neff, R. A. Athale, S. H. Lee, “Two-dimensional spatial light modulators: a tutorial,” Proc. IEEE 78, 826–855 (1990).
[CrossRef]

Lee, S. S.

Lessard, R. A.

Makushenko, A. M.

A. M. Makushenko, B. S. Neporent, O. V. Stolbova, “Reversible orientational photodichroism and photoisomerization of aromatic azo compounds. I: Model of the system,” Opt. Spectrosc. (USSR) 31, 295–299 (1971).

Markovsky, P.

L. Nikolova, P. Markovsky, N. Tomova, V. Dragostinova, N. Mateva, “Optically controlled photo-induced birefringence in photo-anisotropic materials,” J. Mod. Opt. 35, 1789–1799 (1988).
[CrossRef]

Marrakchi, A.

J. W. Yu, D. Psaltis, A. Marrakchi, A. R. Tanguay, R. V. Johnson, “The photorefractive incoherent-to-coherent optical converter,” in Photorefractive Materials and Their Applications II, P. Guinter, J. -P. Huignard, eds. (Springer-Verlag, New York, 1989), pp. 275–323.
[CrossRef]

Mateva, N.

L. Nikolova, P. Markovsky, N. Tomova, V. Dragostinova, N. Mateva, “Optically controlled photo-induced birefringence in photo-anisotropic materials,” J. Mod. Opt. 35, 1789–1799 (1988).
[CrossRef]

Mita, I.

K. Horie, I. Mita, “Reactions and photodynamics in polymer solids,” Adv. Polym. Sci. 88, 77–128 (1989).
[CrossRef]

Neff, J. A.

J. A. Neff, R. A. Athale, S. H. Lee, “Two-dimensional spatial light modulators: a tutorial,” Proc. IEEE 78, 826–855 (1990).
[CrossRef]

Neporent, B. S.

A. M. Makushenko, B. S. Neporent, O. V. Stolbova, “Reversible orientational photodichroism and photoisomerization of aromatic azo compounds. I: Model of the system,” Opt. Spectrosc. (USSR) 31, 295–299 (1971).

Nikolova, L.

L. Nikolova, P. Markovsky, N. Tomova, V. Dragostinova, N. Mateva, “Optically controlled photo-induced birefringence in photo-anisotropic materials,” J. Mod. Opt. 35, 1789–1799 (1988).
[CrossRef]

T. Todorov, L. Nikolova, N. Tomova, “Polarization holography. 1: Anew high efficiency organic material with reversible photoinduced birefringence,” Appl. Opt. 23, 4309–4312 (1984).
[CrossRef] [PubMed]

Perry, P. J.

C. M. Verber, R. E. Schwerzel, P. J. Perry, R. A. Craig, “Holographic recording materials development,” NTIS Rep. N76–23544 (Battelle Memorial Laboratories, Columbus, Ohio, 1976).

Petrov, M. P.

A. A. Kamshilin, M. P. Petrov, “Holographic image conversion in a Bi12SiO20,” Sov. Tech. Phys. Lett. 6, 144–145 (1980).

Psaltis, D.

J. W. Yu, D. Psaltis, A. Marrakchi, A. R. Tanguay, R. V. Johnson, “The photorefractive incoherent-to-coherent optical converter,” in Photorefractive Materials and Their Applications II, P. Guinter, J. -P. Huignard, eds. (Springer-Verlag, New York, 1989), pp. 275–323.
[CrossRef]

Rajbenbach, H.

H. Rajbenbach, “Digital optical processing with photorefractive materials: applications of a parallel half-adder circuit to algorithmic state machines,” J. Appl. Phys. 62, 4675–4681 (1987).
[CrossRef]

Richert, R.

R. Richert, “Analysis of non-exponential first-order reactions,” Chem. Phys. Lett. 118, 534–538 (1985).
[CrossRef]

R. Richert, H. Bässler, “Merocyanine ↔ spiropyran transformation in a polymer matrix: an example of a dispersive chemical reaction,” Chem. Phys. Lett. 116, 302–306 (1985).
[CrossRef]

Saito, S.

T. Tsutsui, A. Hatakeyama, S. Saito, “Analysis of thermal reactions of photochromic species in glassy matrices based on the concept of dispersive processes,” Chem. Phys. Lett. 132, 563–566 (1986).
[CrossRef]

Schwerzel, R. E.

C. M. Verber, R. E. Schwerzel, P. J. Perry, R. A. Craig, “Holographic recording materials development,” NTIS Rep. N76–23544 (Battelle Memorial Laboratories, Columbus, Ohio, 1976).

Silberberg, Y.

I. B. Joseph, Y. Silberberg, “Real time holography through triplet state absorption in organic dyes,” Opt. Commun. 41, 455–458 (1982).
[CrossRef]

Smets, G.

G. Smets, “Photochromic phenomena in the solid phase,” Adv. Polym. Sci. 50, 17–44 (1983).
[CrossRef]

Stolbova, O. V.

A. M. Makushenko, B. S. Neporent, O. V. Stolbova, “Reversible orientational photodichroism and photoisomerization of aromatic azo compounds. I: Model of the system,” Opt. Spectrosc. (USSR) 31, 295–299 (1971).

Tanguay, A. R.

A. R. Tanguay, “Materials requirements for optical processing and computing devices,” Opt. Eng. 24, 2–18 (1985).

J. W. Yu, D. Psaltis, A. Marrakchi, A. R. Tanguay, R. V. Johnson, “The photorefractive incoherent-to-coherent optical converter,” in Photorefractive Materials and Their Applications II, P. Guinter, J. -P. Huignard, eds. (Springer-Verlag, New York, 1989), pp. 275–323.
[CrossRef]

Todorov, T.

Tomova, N.

L. Nikolova, P. Markovsky, N. Tomova, V. Dragostinova, N. Mateva, “Optically controlled photo-induced birefringence in photo-anisotropic materials,” J. Mod. Opt. 35, 1789–1799 (1988).
[CrossRef]

T. Todorov, L. Nikolova, N. Tomova, “Polarization holography. 1: Anew high efficiency organic material with reversible photoinduced birefringence,” Appl. Opt. 23, 4309–4312 (1984).
[CrossRef] [PubMed]

Tsutsui, T.

T. Tsutsui, A. Hatakeyama, S. Saito, “Analysis of thermal reactions of photochromic species in glassy matrices based on the concept of dispersive processes,” Chem. Phys. Lett. 132, 563–566 (1986).
[CrossRef]

Verber, C. M.

C. M. Verber, R. E. Schwerzel, P. J. Perry, R. A. Craig, “Holographic recording materials development,” NTIS Rep. N76–23544 (Battelle Memorial Laboratories, Columbus, Ohio, 1976).

Wang, C. H.

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1987), pp. 548–549.

Yu, J. W.

J. W. Yu, D. Psaltis, A. Marrakchi, A. R. Tanguay, R. V. Johnson, “The photorefractive incoherent-to-coherent optical converter,” in Photorefractive Materials and Their Applications II, P. Guinter, J. -P. Huignard, eds. (Springer-Verlag, New York, 1989), pp. 275–323.
[CrossRef]

Adv. Polym. Sci.

G. Smets, “Photochromic phenomena in the solid phase,” Adv. Polym. Sci. 50, 17–44 (1983).
[CrossRef]

K. Horie, I. Mita, “Reactions and photodynamics in polymer solids,” Adv. Polym. Sci. 88, 77–128 (1989).
[CrossRef]

Appl. Opt.

Bell Syst. Tech. J.

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).

Chem. Phys. Lett.

R. Richert, “Analysis of non-exponential first-order reactions,” Chem. Phys. Lett. 118, 534–538 (1985).
[CrossRef]

R. Richert, H. Bässler, “Merocyanine ↔ spiropyran transformation in a polymer matrix: an example of a dispersive chemical reaction,” Chem. Phys. Lett. 116, 302–306 (1985).
[CrossRef]

T. Tsutsui, A. Hatakeyama, S. Saito, “Analysis of thermal reactions of photochromic species in glassy matrices based on the concept of dispersive processes,” Chem. Phys. Lett. 132, 563–566 (1986).
[CrossRef]

J. Appl. Phys.

H. Rajbenbach, “Digital optical processing with photorefractive materials: applications of a parallel half-adder circuit to algorithmic state machines,” J. Appl. Phys. 62, 4675–4681 (1987).
[CrossRef]

J. Mod. Opt.

L. Nikolova, P. Markovsky, N. Tomova, V. Dragostinova, N. Mateva, “Optically controlled photo-induced birefringence in photo-anisotropic materials,” J. Mod. Opt. 35, 1789–1799 (1988).
[CrossRef]

Opt. Commun.

I. B. Joseph, Y. Silberberg, “Real time holography through triplet state absorption in organic dyes,” Opt. Commun. 41, 455–458 (1982).
[CrossRef]

Opt. Eng.

A. R. Tanguay, “Materials requirements for optical processing and computing devices,” Opt. Eng. 24, 2–18 (1985).

Opt. Lett.

Opt. Spectrosc. (USSR)

Sh. D. Kakichashvili, “Regularity in photoanisotropic phenomena,” Opt. Spectrosc. (USSR) 52, 191–194 (1982).

A. M. Makushenko, B. S. Neporent, O. V. Stolbova, “Reversible orientational photodichroism and photoisomerization of aromatic azo compounds. I: Model of the system,” Opt. Spectrosc. (USSR) 31, 295–299 (1971).

Proc. IEEE

J. A. Neff, R. A. Athale, S. H. Lee, “Two-dimensional spatial light modulators: a tutorial,” Proc. IEEE 78, 826–855 (1990).
[CrossRef]

Sov. J. Quantum Electron.

Sh. D. Kakichashvili, “Polarization-holographic recording in the general case of a reaction of a photoanisotropic medium,” Sov. J. Quantum Electron. 13, 1317–1319 (1983).
[CrossRef]

Sov. Tech. Phys. Lett.

A. A. Kamshilin, M. P. Petrov, “Holographic image conversion in a Bi12SiO20,” Sov. Tech. Phys. Lett. 6, 144–145 (1980).

Other

H. J. Caulfield, W. T. Cathey, “Spatial light modulator and process of modulation,” U.S. Patent4,429,954 (7February1984).

J. W. Yu, D. Psaltis, A. Marrakchi, A. R. Tanguay, R. V. Johnson, “The photorefractive incoherent-to-coherent optical converter,” in Photorefractive Materials and Their Applications II, P. Guinter, J. -P. Huignard, eds. (Springer-Verlag, New York, 1989), pp. 275–323.
[CrossRef]

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1987), pp. 548–549.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), pp. 110–120.

R. Kingslake, Optical System Design (Academic, New York, 1983), pp. 269–272.

C. M. Verber, R. E. Schwerzel, P. J. Perry, R. A. Craig, “Holographic recording materials development,” NTIS Rep. N76–23544 (Battelle Memorial Laboratories, Columbus, Ohio, 1976).

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Figures (14)

Fig. 1
Fig. 1

(a) Simplified three-level energy diagram for methyl orange dye molecules, (b) transcis isomerization of methyl orange ISC, intersystem conversion..

Fig. 2
Fig. 2

(a) Spatial orientation of a dye molecule with respect to the polarization state of the exciting light; (b) transition probability for a dye molecule at a given orientation that is obtained by the radial length from the center to the surface at that orientation, which is in turn obtained by σ/σ|; the parameters are a2 = 0.7, b2 = 0.3, and σ = 0.

Fig. 3
Fig. 3

MO/PVA film absorption spectra: curve a is without additional strong optical excitation, and curve b is under weak optical excitation by a filtered white-light source centered at 510 nm with a 10-nm bandwidth. The sample used has a thickness of 0.30 mm and a dye concentration of 0.06 wt. %. Much stronger bleaching can be obtained with an Ar+ laser.

Fig. 4
Fig. 4

Formation of a polarization hologram: d, thickness of MO/PVA film; r, reference beam; s, signal beam.

Fig. 5
Fig. 5

Schematic diagram illustrating the PAICOC process: (a) PAICOC writing, (b) PAICOC readout.

Fig. 6
Fig. 6

Simulation results of PAICOC diffraction efficiency. The parameters used are κ ^ = 0, α0 = 3.6 mm−1, d = 0.22 mm, κ ^ /2∊0n0 = −(133.3 + i6.14) × 10−4 mm2/mW, I s = 0.15 mW/mm2, I g = 0.35 mW/mm2, m g = 0.9, m i = 0.9, θ = π/8, and Δk = 0. The approximate results are from the analytic solutions obtained by Eqs. (25) and (39)(44) and are rescaled using the axis on the right.

Fig. 7
Fig. 7

Diffraction efficiency and modulation depth versus incoherent beam intensity; the parameters used in the simulation are the same as in Fig. 6.

Fig. 8
Fig. 8

Arrangement of PAICOC experiments: M’s, mirrors; BE&SF, beam expander and spatial filter; DI’s, diaphragms; CL, collimation lens; BS, beam splitter; L, condensing lens; LP’s, linear polarizers; O, object to be converted; S, sample; IL’s, imaging lenses.

Fig. 9
Fig. 9

Converted negative coherent images: (a) U.S. Air Force resolution target, (b) enlarged central part of (a), (c) zebra picture, (d) student picture from a negative.

Fig. 10
Fig. 10

Converted coherent Ronchi-ruling images (left) and cross sections through their optical Fourier spectra (right) obtained on a CCD camera: (a) horizontally oriented situation, (b) vertically oriented situation. The d and first-order diffractions are completely saturated.

Fig. 11
Fig. 11

(a) Geometrical resolution limitation of the converted coherent image at angle θ, (b) telescopic imaging geometry required to eliminate keystone distortion of a tilted object plane.

Fig. 12
Fig. 12

(a) Wave-vector diagram in real space, (b) Bragg-mismatch diagram in momentum space for vertically oriented line pairs with a horizontal grating vector.

Fig. 13
Fig. 13

Wave-vector diagram in real space, (b) Momentum space representation of wave and grating vectors for horizontally oriented line pairs with a vertical grating vector.

Fig. 14
Fig. 14

Geometric limitation of resolution imposed by the finite intersection area. W is the minimum resolvable spot size.

Equations (45)

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

σ = σ ( a 2 cos 2 θ + b 2 sin 2 θ cos 2 ϕ ) + σ [ a 2 sin 2 θ + b 2 ( 1 - sin 2 θ cos 2 ϕ ) ] ,
^ _ _ = [ ^ 0 + κ ^ a 2 + κ ^ b 2 i κ ^ c S 3 - i κ ^ c S 3 ^ 0 + κ ^ a 2 + κ ^ b 2 ] .
a 2 = ½ ( J x x + J y y ) + ½ [ ( J x x + J y y ) 2 + ( J x y - J y x ) 2 ] 1 / 2 ,
b 2 = ½ ( J x x + J y y ) - ½ [ ( J x x + J y y ) 2 + ( J x y - J y x ) 2 ] 1 / 2 ,
S 3 = i ( J y x - J x y ) ,
J x x ( y ) = I g [ 1 + m g cos ( k g y + φ ) ] ,
sin 2 γ ( y ) = J x y ( y ) + J y x ( y ) a 2 ( y ) - b 2 ( y ) ,
cos 2 γ ( y ) = J x x ( y ) - J y y ( y ) a 2 ( y ) - b 2 ( y ) .
^ _ _ = R [ - γ ( y ) ] ^ _ _ R [ γ ( y ) ] ,
R [ γ ( y ) ] = [ cos γ ( y ) sin γ ( y ) - sin γ ( y ) cos γ ( y ) ] ,
^ _ _ = [ ^ 0 + κ ^ J x x ( y ) + κ ^ J y y ( y ) ½ ( κ ^ - κ ^ ) [ J x y ( y ) + J y x ( y ) ] + κ ^ c [ J x y ( y ) - J y x ( y ) ] ½ ( κ ^ - κ ^ ) [ J x y ( y ) + J y x ( y ) ] - κ ^ c [ J x y ( y ) - J y x ( y ) ] ^ 0 + κ ^ J x x ( y ) + κ ^ J y y ( y ) ] .
^ _ _ = [ ^ 0 + κ ^ J x x + κ ^ J y y 1 + Tr ( J ) / I s ½ ( κ ^ - κ ^ ) ( J x y + J y x ) + κ ^ c ( J x y - J y x ) 1 + Tr ( J ) / I s ½ ( κ ^ - κ ^ ) ( J x y + J y x ) - κ ^ c ( J x y - J y x ) 1 + Tr ( J ) / I s ^ 0 + κ ^ J x x + κ ^ J y y 1 + Tr ( J ) / I s ] .
^ _ _ = [ ^ 0 + κ ^ J x x 1 + J x x / I s 0 0 ^ 0 + κ ^ J x x 1 + J x x / I s ] .
^ _ _ = [ ^ x , 0 + ^ x , 1 cos ( k g y ) 0 0 ^ y , 0 + ^ y , 1 cos ( k g y ) ] ,
^ x , 0 = ^ 0 + κ ^ I s { 1 - I s [ ( I s + I 1 + I 2 ) 2 - 4 I 1 I 2 ] 1 / 2 } ,
^ x , 1 = κ ^ I s 2 ( I 1 I 2 ) 1 / 2 { I s + I 1 + I 2 [ ( I s + I 1 + I 2 ) 2 - 4 I 1 I 2 ] 1 / 2 - 1 } ,
^ y , 0 = ^ 0 + κ ^ I s { 1 - I s [ ( I s + I 1 + I 2 ) 2 - 4 I 1 I 2 ] 1 / 2 } ,
^ y , 1 = κ ^ I s 2 ( I 1 I 2 ) 1 / 2 { I s + I 1 + I 2 [ ( I s + I 1 + I 2 ) 2 - 4 I 1 I 2 ] 1 / 2 - 1 } ,
n ^ 0 = ( ^ 0 0 ) 1 / 2 ,
Δ n ^ Δ ^ 2 0 n 0 ,
n x , 0 = n 0 + κ I s 2 0 n 0 { 1 - I s [ ( I s + I 1 + I 2 ) 2 - 4 I 1 I 2 ] 1 / 2 } ,
α x , 0 = α 0 + π κ I s λ 0 0 n 0 { 1 - I s [ ( I s + I 1 + I 2 ) 2 - 4 I 1 I 2 ] 1 / 2 } ,
n x , 1 = κ I s 2 2 0 n 0 ( I 1 I 2 ) 1 / 2 { I s + I 1 + I 2 [ ( I s + I 1 + I 2 ) 2 - 4 I 1 I 2 ] 1 / 2 - 1 } ,
α x , 1 = π κ I s 2 λ 0 0 n 0 ( I 1 I 2 ) 1 / 2 { I s + I 1 + I 2 [ ( I s + I 1 + I 2 ) 2 - 4 I 1 I 2 ] 1 / 2 - 1 } ,
η x = exp ( - 2 α x , 0 d cos θ ) [ sin 2 ( π n x , 1 d λ cos θ ) + sinh 2 ( α x , 1 d 2 cos θ ) ] ,
η y = exp ( - 2 α y , 0 d cos θ ) [ sin 2 ( cos 2 θ π n y , 1 d λ cos θ ) + sinh 2 ( cos 2 θ α y , 1 d 2 cos θ ) ] ,
^ _ _ = [ ^ 0 + κ ^ J x x + κ ^ J y y + ½ ( κ ^ + κ ^ ) I in ( x , y ) 1 + [ Tr ( J ) + I in ( x , y ) / ] I s ½ ( κ ^ - κ ^ ) ( J x y + J y x ) + κ ^ c ( J x y - J y x ) 1 + [ Tr ( J ) + I in ( x , y ) ] / I s ½ ( κ ^ - κ ^ ) ( J x y + J y x ) - κ ^ c ( J x y - J y x ) 1 + [ Tr ( J ) + I in ( x , y ) ] / I s ^ 0 + κ ^ J x x + κ ^ J y y + ½ ( κ ^ + κ ^ ) I in ( x , y ) 1 + [ Tr ( J ) + I in ( x , y ) ] / I s ] ,
^ _ _ [ ^ 0 + ½ ( κ ^ + κ ^ ) I s 0 0 ^ 0 + ½ ( κ ^ + κ ^ ) I s ] .
^ _ _ = [ ^ 0 + κ ^ J x x + ½ ( κ ^ + κ ^ ) I in ( x , y ) 1 + [ J x x + I in ( x , y ) ] / I s 0 0 ^ 0 + κ ^ J x x + ½ ( κ ^ + κ ^ ) I in ( x , y ) 1 + [ J x x + I in ( x , y ) ] / I s ] ,
^ _ _ = [ ^ x , 0 + ^ x , i cos ( k i y ) + ^ x , g cos ( k g y ) + 2 ^ x , c cos ( k i y ) cos ( k g y ) 0 0 ^ y , 0 + ^ y , i cos ( k i y ) + ^ y , g cos ( k g y ) + 2 ^ y , c cos ( k i y ) cos ( k g y ) ] ,
^ x , 0 = 1 a 0 a 2 π / k i ^ 11 d y ,
^ x , i = 1 a 0 a 2 π / k i ^ 11 cos ( k i y ) d y ,
^ x , g = 1 a 0 a 2 π / k i ^ 11 cos ( k g y ) d y ,
^ x , c = 1 a 0 a 2 π / k i ^ 11 cos ( k g y ) cos ( k i y ) d y .
^ x , 0 = ^ 0 + [ κ ^ I g + ½ ( κ ^ + κ ^ ) I i ] I s I s + I g + I i ,
^ x , i = 1 2 I i m i I s [ ( κ ^ - κ ^ ) I g + ( κ ^ + κ ^ ) I s ] ( I s + I g + I i ) 2 ,
^ x , g = I g m g I s [ ½ ( κ ^ - κ ^ ) I i + κ ^ I s ] ( I s + I g + I i ) 2 ,
^ x , c = - 1 4 ( κ ^ - κ ^ ) I i m i I g m g I s ( I s + I g + I i ) 2 .
α x , 0 = α 0 + π [ κ I g + ½ ( κ + κ ) I i ] I s λ 0 0 n 0 ( I s + I g + I i ) ,
α x , g = π I g m g I s [ ½ ( κ - κ ) I i + κ I s ] λ 0 0 n 0 ( I s + I g + I i ) 2 ,
n x , g = I g m g I s [ ½ ( κ - κ ) I i + κ I s ] 2 0 n 0 ( I s + I g + I i ) 2 ,
α x , c = - 1 4 π ( κ - κ ) I i m i I g m g I s λ 0 0 n 0 ( I s + I g + I i ) 2 ,
n x , c = - 1 8 ( κ - κ ) I i m i I g m g I s 0 n 0 ( I s + I g + I i ) 2 .
I co ( x , y ) = I readout ( n x , g ) 1 / 2 + 2 ( η x , c ) 1 / 2 cos ( k i y ) 2 = I readout [ ( η x , g + 2 η x , c ) + 4 ( η x , g η x , c ) ½ cos ( k i y ) + 2 η x , c cos ( 2 k i y ) ] = I readout [ η ( 0 ) + η ( 1 ) cos ( k i y ) + η ( 2 ) cos ( 2 k i y ) ] ,
m = 4 ( η x , g η x , c ) 1 / 2 η x , g + 4 η x , c .

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