Abstract

Image formation in a quasi-linear isoplanar system consisting of a plane-parallel layer of bronze (a “magic mirror”) and a plane-parallel layer of free space (air) is described. The exhaustive characteristic of the quasi-linear isoplanar system is performed with a point spread function, where the role of an incoming signal from a point source is investigated with a local camber (or a hollow) on the back of the bronze mirror. Note that the point spread function of the image system should be as close as possible to a Dirac δ function. The quasi-linear isoplanar imaging magic-mirror–layer-of-space system should map a point source input signal (local camber on the back surface of a bronze mirror) to a point output signal (a light point on the screen). At a certain parity between the thickness of the layer of bronze and the thickness of the layer of free space, this linear isoplanar system forms the image with a very large depth of field.

© 2009 Optical Society of America

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References

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  1. D. Brewster, “Account of a curious Chinese mirror, which reflects from its polished face the figures embossed upon its back,” London Edinburgh Philos. Mag. J. Sci. 1, 438-441(1832).
  2. G. Saines and M. G. Tomilin, “Magic mirrors of the Orient,” J. Opt. Technol. 66, 758-765 (1999).
    [CrossRef]
  3. Magic Mirrors in Grand Illusions, http://www.grand-illusions.com/articles/magic_mirror/.
  4. W. E. Ayrton and J. Perry, “The magic mirror of Japan,” Proc. R. Soc. London 28, 127-148 (1878-1879).
    [CrossRef]
  5. M. V. Berry, “Oriental magic mirrors and the Laplacian image,” Eur. J. Phys. 27, 109-118 (2006).
    [CrossRef]
  6. S.-y. Mak and D.-y. Yip, “Secrets of the Chinese magic mirror replica,” Phys. Educ. 102-107 (2001).
    [CrossRef]
  7. P. Blaustein and S. Hahn, “Realtime inspection of wafer surfaces,” Solid State Technol. 32(12), 27-29 (1989).
  8. K. Kugimiya, “Characterization of polished surfaces by 'Makyoh',” J. Cryst. Growth 103, 461-468 (1990).
    [CrossRef]
  9. F. Riesz, “Geometrical optical model of the image formation in Makyoh (magic-mirror) topography,” J. Phys. D 33, 3033-3040 (2000).
    [CrossRef]
  10. F. Riesz, “Makyoh topography for the morphological study of compound semiconductor wafers and structures,” Mater. Sci. Eng. B 80, 220-223 (2001).
    [CrossRef]
  11. D. Korytár and M. Hrivnák, “Experimental and computer simulated Makyoh images of semiconductor wafers,” Jpn. J. Appl. Phys. 32, 693-698 (1993).
    [CrossRef]
  12. Z. J. Laczik, “Quantitative Makyoh topography,” Opt. Eng. 39, 2562-2567 (2000).
    [CrossRef]
  13. J. Goodman, Introduction to Fourier Optics (Roberts, 2005).
  14. O. N. Litvinenko, Osnovy radiooptiki (Fundaments of Radiooptics) (Teknika, 1974) [in Russian].
  15. A. V. Gitin, “Iconics--a comprehensive approach to optics,” J. Opt. Technol. 65, 141-142 (1998).
  16. E. W. H. Selwyn, “Combination of lens and film,” in Applied Optics and Optical Engineering Volume II--the Detection of Light and Infrared Radiation, R. Kingslake, ed. (Academic1965), pp. 165-194.
  17. J. M. Lloyd, Thermal Imaging Systems (Plenum, 1975).
  18. K. Hibino, M. Yamauchi, M. Katoh, and K. Matsuda, “Modern technique for the production and measurement of Makyoh images,” J. Cryst. Growth 103, 433-436 (1990).
    [CrossRef]
  19. S. Tokura, N. Fujino, M. Ninomiya, and K. Masuda, “Characterization of mirror-polished silicon wafers by Makyoh method,” J. Cryst. Growth 103, 437-442 (1990).
    [CrossRef]
  20. A. V. Gitin, “Optical systems for measuring the Wigner function of a laser beam by the method of phase-spatial tomography,” Quantum Electron. 37, 85-91 (2007).
    [CrossRef]
  21. W. J. Smith,” Modern Optical Engineering (McGraw-Hill, 2000).
  22. V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10, 509-514 (1968).
    [CrossRef]
  23. J. B. Pendry “Negative refraction index makes perfect lens,” Phys. Rev. Lett. 85, 3966-3969 (2000).
    [CrossRef] [PubMed]
  24. J. B. Pendry and D. R. Smith,“Reversing light with negative refraction,” Phys. Today 57(6), 37-43 (2004).
    [CrossRef]

2007 (1)

A. V. Gitin, “Optical systems for measuring the Wigner function of a laser beam by the method of phase-spatial tomography,” Quantum Electron. 37, 85-91 (2007).
[CrossRef]

2006 (1)

M. V. Berry, “Oriental magic mirrors and the Laplacian image,” Eur. J. Phys. 27, 109-118 (2006).
[CrossRef]

2004 (1)

J. B. Pendry and D. R. Smith,“Reversing light with negative refraction,” Phys. Today 57(6), 37-43 (2004).
[CrossRef]

2001 (2)

F. Riesz, “Makyoh topography for the morphological study of compound semiconductor wafers and structures,” Mater. Sci. Eng. B 80, 220-223 (2001).
[CrossRef]

S.-y. Mak and D.-y. Yip, “Secrets of the Chinese magic mirror replica,” Phys. Educ. 102-107 (2001).
[CrossRef]

2000 (3)

F. Riesz, “Geometrical optical model of the image formation in Makyoh (magic-mirror) topography,” J. Phys. D 33, 3033-3040 (2000).
[CrossRef]

Z. J. Laczik, “Quantitative Makyoh topography,” Opt. Eng. 39, 2562-2567 (2000).
[CrossRef]

J. B. Pendry “Negative refraction index makes perfect lens,” Phys. Rev. Lett. 85, 3966-3969 (2000).
[CrossRef] [PubMed]

1999 (1)

1998 (1)

A. V. Gitin, “Iconics--a comprehensive approach to optics,” J. Opt. Technol. 65, 141-142 (1998).

1993 (1)

D. Korytár and M. Hrivnák, “Experimental and computer simulated Makyoh images of semiconductor wafers,” Jpn. J. Appl. Phys. 32, 693-698 (1993).
[CrossRef]

1990 (3)

K. Hibino, M. Yamauchi, M. Katoh, and K. Matsuda, “Modern technique for the production and measurement of Makyoh images,” J. Cryst. Growth 103, 433-436 (1990).
[CrossRef]

S. Tokura, N. Fujino, M. Ninomiya, and K. Masuda, “Characterization of mirror-polished silicon wafers by Makyoh method,” J. Cryst. Growth 103, 437-442 (1990).
[CrossRef]

K. Kugimiya, “Characterization of polished surfaces by 'Makyoh',” J. Cryst. Growth 103, 461-468 (1990).
[CrossRef]

1989 (1)

P. Blaustein and S. Hahn, “Realtime inspection of wafer surfaces,” Solid State Technol. 32(12), 27-29 (1989).

1968 (1)

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10, 509-514 (1968).
[CrossRef]

1832 (1)

D. Brewster, “Account of a curious Chinese mirror, which reflects from its polished face the figures embossed upon its back,” London Edinburgh Philos. Mag. J. Sci. 1, 438-441(1832).

Ayrton, W. E.

W. E. Ayrton and J. Perry, “The magic mirror of Japan,” Proc. R. Soc. London 28, 127-148 (1878-1879).
[CrossRef]

Berry, M. V.

M. V. Berry, “Oriental magic mirrors and the Laplacian image,” Eur. J. Phys. 27, 109-118 (2006).
[CrossRef]

Blaustein, P.

P. Blaustein and S. Hahn, “Realtime inspection of wafer surfaces,” Solid State Technol. 32(12), 27-29 (1989).

Brewster, D.

D. Brewster, “Account of a curious Chinese mirror, which reflects from its polished face the figures embossed upon its back,” London Edinburgh Philos. Mag. J. Sci. 1, 438-441(1832).

Fujino, N.

S. Tokura, N. Fujino, M. Ninomiya, and K. Masuda, “Characterization of mirror-polished silicon wafers by Makyoh method,” J. Cryst. Growth 103, 437-442 (1990).
[CrossRef]

Gitin, A. V.

A. V. Gitin, “Optical systems for measuring the Wigner function of a laser beam by the method of phase-spatial tomography,” Quantum Electron. 37, 85-91 (2007).
[CrossRef]

A. V. Gitin, “Iconics--a comprehensive approach to optics,” J. Opt. Technol. 65, 141-142 (1998).

Goodman, J.

J. Goodman, Introduction to Fourier Optics (Roberts, 2005).

Hahn, S.

P. Blaustein and S. Hahn, “Realtime inspection of wafer surfaces,” Solid State Technol. 32(12), 27-29 (1989).

Hibino, K.

K. Hibino, M. Yamauchi, M. Katoh, and K. Matsuda, “Modern technique for the production and measurement of Makyoh images,” J. Cryst. Growth 103, 433-436 (1990).
[CrossRef]

Hrivnák, M.

D. Korytár and M. Hrivnák, “Experimental and computer simulated Makyoh images of semiconductor wafers,” Jpn. J. Appl. Phys. 32, 693-698 (1993).
[CrossRef]

Katoh, M.

K. Hibino, M. Yamauchi, M. Katoh, and K. Matsuda, “Modern technique for the production and measurement of Makyoh images,” J. Cryst. Growth 103, 433-436 (1990).
[CrossRef]

Korytár, D.

D. Korytár and M. Hrivnák, “Experimental and computer simulated Makyoh images of semiconductor wafers,” Jpn. J. Appl. Phys. 32, 693-698 (1993).
[CrossRef]

Kugimiya, K.

K. Kugimiya, “Characterization of polished surfaces by 'Makyoh',” J. Cryst. Growth 103, 461-468 (1990).
[CrossRef]

Laczik, Z. J.

Z. J. Laczik, “Quantitative Makyoh topography,” Opt. Eng. 39, 2562-2567 (2000).
[CrossRef]

Litvinenko, O. N.

O. N. Litvinenko, Osnovy radiooptiki (Fundaments of Radiooptics) (Teknika, 1974) [in Russian].

Lloyd, J. M.

J. M. Lloyd, Thermal Imaging Systems (Plenum, 1975).

Mak, S.-y.

S.-y. Mak and D.-y. Yip, “Secrets of the Chinese magic mirror replica,” Phys. Educ. 102-107 (2001).
[CrossRef]

Masuda, K.

S. Tokura, N. Fujino, M. Ninomiya, and K. Masuda, “Characterization of mirror-polished silicon wafers by Makyoh method,” J. Cryst. Growth 103, 437-442 (1990).
[CrossRef]

Matsuda, K.

K. Hibino, M. Yamauchi, M. Katoh, and K. Matsuda, “Modern technique for the production and measurement of Makyoh images,” J. Cryst. Growth 103, 433-436 (1990).
[CrossRef]

Ninomiya, M.

S. Tokura, N. Fujino, M. Ninomiya, and K. Masuda, “Characterization of mirror-polished silicon wafers by Makyoh method,” J. Cryst. Growth 103, 437-442 (1990).
[CrossRef]

Pendry, J. B.

J. B. Pendry and D. R. Smith,“Reversing light with negative refraction,” Phys. Today 57(6), 37-43 (2004).
[CrossRef]

J. B. Pendry “Negative refraction index makes perfect lens,” Phys. Rev. Lett. 85, 3966-3969 (2000).
[CrossRef] [PubMed]

Perry, J.

W. E. Ayrton and J. Perry, “The magic mirror of Japan,” Proc. R. Soc. London 28, 127-148 (1878-1879).
[CrossRef]

Riesz, F.

F. Riesz, “Makyoh topography for the morphological study of compound semiconductor wafers and structures,” Mater. Sci. Eng. B 80, 220-223 (2001).
[CrossRef]

F. Riesz, “Geometrical optical model of the image formation in Makyoh (magic-mirror) topography,” J. Phys. D 33, 3033-3040 (2000).
[CrossRef]

Saines, G.

Selwyn, E. W. H.

E. W. H. Selwyn, “Combination of lens and film,” in Applied Optics and Optical Engineering Volume II--the Detection of Light and Infrared Radiation, R. Kingslake, ed. (Academic1965), pp. 165-194.

Smith, D. R.

J. B. Pendry and D. R. Smith,“Reversing light with negative refraction,” Phys. Today 57(6), 37-43 (2004).
[CrossRef]

Smith, W. J.

W. J. Smith,” Modern Optical Engineering (McGraw-Hill, 2000).

Tokura, S.

S. Tokura, N. Fujino, M. Ninomiya, and K. Masuda, “Characterization of mirror-polished silicon wafers by Makyoh method,” J. Cryst. Growth 103, 437-442 (1990).
[CrossRef]

Tomilin, M. G.

Veselago, V. G.

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10, 509-514 (1968).
[CrossRef]

Yamauchi, M.

K. Hibino, M. Yamauchi, M. Katoh, and K. Matsuda, “Modern technique for the production and measurement of Makyoh images,” J. Cryst. Growth 103, 433-436 (1990).
[CrossRef]

Yip, D.-y.

S.-y. Mak and D.-y. Yip, “Secrets of the Chinese magic mirror replica,” Phys. Educ. 102-107 (2001).
[CrossRef]

Eur. J. Phys. (1)

M. V. Berry, “Oriental magic mirrors and the Laplacian image,” Eur. J. Phys. 27, 109-118 (2006).
[CrossRef]

J. Cryst. Growth (3)

K. Kugimiya, “Characterization of polished surfaces by 'Makyoh',” J. Cryst. Growth 103, 461-468 (1990).
[CrossRef]

K. Hibino, M. Yamauchi, M. Katoh, and K. Matsuda, “Modern technique for the production and measurement of Makyoh images,” J. Cryst. Growth 103, 433-436 (1990).
[CrossRef]

S. Tokura, N. Fujino, M. Ninomiya, and K. Masuda, “Characterization of mirror-polished silicon wafers by Makyoh method,” J. Cryst. Growth 103, 437-442 (1990).
[CrossRef]

J. Opt. Technol. (2)

G. Saines and M. G. Tomilin, “Magic mirrors of the Orient,” J. Opt. Technol. 66, 758-765 (1999).
[CrossRef]

A. V. Gitin, “Iconics--a comprehensive approach to optics,” J. Opt. Technol. 65, 141-142 (1998).

J. Phys. D (1)

F. Riesz, “Geometrical optical model of the image formation in Makyoh (magic-mirror) topography,” J. Phys. D 33, 3033-3040 (2000).
[CrossRef]

Jpn. J. Appl. Phys. (1)

D. Korytár and M. Hrivnák, “Experimental and computer simulated Makyoh images of semiconductor wafers,” Jpn. J. Appl. Phys. 32, 693-698 (1993).
[CrossRef]

London Edinburgh Philos. Mag. J. Sci. (1)

D. Brewster, “Account of a curious Chinese mirror, which reflects from its polished face the figures embossed upon its back,” London Edinburgh Philos. Mag. J. Sci. 1, 438-441(1832).

Mater. Sci. Eng. B (1)

F. Riesz, “Makyoh topography for the morphological study of compound semiconductor wafers and structures,” Mater. Sci. Eng. B 80, 220-223 (2001).
[CrossRef]

Opt. Eng. (1)

Z. J. Laczik, “Quantitative Makyoh topography,” Opt. Eng. 39, 2562-2567 (2000).
[CrossRef]

Phys. Educ. (1)

S.-y. Mak and D.-y. Yip, “Secrets of the Chinese magic mirror replica,” Phys. Educ. 102-107 (2001).
[CrossRef]

Phys. Rev. Lett. (1)

J. B. Pendry “Negative refraction index makes perfect lens,” Phys. Rev. Lett. 85, 3966-3969 (2000).
[CrossRef] [PubMed]

Phys. Today (1)

J. B. Pendry and D. R. Smith,“Reversing light with negative refraction,” Phys. Today 57(6), 37-43 (2004).
[CrossRef]

Proc. R. Soc. London (1)

W. E. Ayrton and J. Perry, “The magic mirror of Japan,” Proc. R. Soc. London 28, 127-148 (1878-1879).
[CrossRef]

Quantum Electron. (1)

A. V. Gitin, “Optical systems for measuring the Wigner function of a laser beam by the method of phase-spatial tomography,” Quantum Electron. 37, 85-91 (2007).
[CrossRef]

Solid State Technol. (1)

P. Blaustein and S. Hahn, “Realtime inspection of wafer surfaces,” Solid State Technol. 32(12), 27-29 (1989).

Sov. Phys. Usp. (1)

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10, 509-514 (1968).
[CrossRef]

Other (6)

E. W. H. Selwyn, “Combination of lens and film,” in Applied Optics and Optical Engineering Volume II--the Detection of Light and Infrared Radiation, R. Kingslake, ed. (Academic1965), pp. 165-194.

J. M. Lloyd, Thermal Imaging Systems (Plenum, 1975).

Magic Mirrors in Grand Illusions, http://www.grand-illusions.com/articles/magic_mirror/.

W. J. Smith,” Modern Optical Engineering (McGraw-Hill, 2000).

J. Goodman, Introduction to Fourier Optics (Roberts, 2005).

O. N. Litvinenko, Osnovy radiooptiki (Fundaments of Radiooptics) (Teknika, 1974) [in Russian].

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Figures (6)

Fig. 1
Fig. 1

Point camber on the back surface of a bronze mirror h back ( x , y ) = δ ( x , y ) is mapped onto a Gaussian hollow on the reflecting surface g z ( x + ξ , y ) .

Fig. 2
Fig. 2

Concave parabolic mirror with vertex at point ( x + ξ , y ) and focal length f = z is mapped onto a light point on the screen surface δ ( x + ξ , y ) .

Fig. 3
Fig. 3

Approximation of Gaussian curve z = ( 1 / 2 π σ ) exp [ ( x x ) 2 / 2 σ 2 ] by a parabola z = 1 / 2 π σ ( 1 / 4 f ) ( x x ) 2 .

Fig. 4
Fig. 4

Mapping of the point camber to the back surface of a mirror in the focused light point on the screen in the magic- mirror–layer-of-free-space system.

Fig. 5
Fig. 5

Superlens.

Fig. 6
Fig. 6

Magnification of the convex-magic-mirror–concentric-layer-of-free-space system.

Equations (19)

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U ( x , y ) = L { U ( x , y ) } .
U ( x , y ) = R 2 U ( ξ , η ) δ ( x ξ , y η ) d ξ d η .
U ( x , y ) = L { R 2 U ( ξ , η ) δ ( x ξ , y η ) d ξ d η } = R 2 U ( ξ , η ) L { δ ( x ξ , y η ) } d ξ d η .
U ( x , y ) = R 2 U ( ξ , η ) g ( x , y , ξ , η ) d ξ d η ,
U ( x , y ) = R 2 U ( x , y ) g ( x , y , x , y ) d x d y .
g ( x , y , x , y ) = g ( x x , y y ) .
U ( x , y ) = R 2 U ( x , y ) g ( x y , y ) d x d y ( U * g ) ( x , y ) .
h front ( x , y ) = R 2 h back ( x , y ) g z ( x x , y y ) d x d y ( h back * g z ) ( x , y ) ,
g z ( x x , y y ) = 1 2 π σ 2 exp { ( x x ) 2 + ( y y ) 2 2 σ 2 }
h front ( x , y ) = R 2 δ ( x , y ) g z ( x x , y y ) d x d y = 1 2 π σ 2 exp { ( x x ) 2 + ( y y ) 2 2 σ 2 } .
U front ( x , y ) = t ( x , y ) U ( x , y ) ,
U out ( x , y ) = R 2 U front ( x , y ) g z ( x x , y y ) d x d y ( U front * g z ) ( x , y ) ,
g z ( x x , y y ) Const × exp { i k ( x x ) 2 ( y y ) 2 2 z }
t ( x x , y y ) = exp { i k ( x x ) 2 + ( y y ) 2 2 f } ,
U out ( x , y ) = Const R 2 U ( x , y ) exp { i k x ( x x ) + y ( y y ) f } d x d y ,
U out ( x , y ) = Const R 2 exp { i k x sin θ } exp ( i k ( x x ) 2 + ( y y ) 2 2 f ) d x d y = Const δ ( x + f sin θ , y ) .
U out ( x , y ) = R 2 h back ( x , y ) G ( x x , y y ) d x d y ( h back * G ) ( x , y ) ,
h front ( x x , y y ) = 1 2 π σ 2 exp { ( x x ) 2 + ( y y ) 2 2 σ 2 } 1 2 π σ 2 [ ( x x ) 2 + ( y y ) 2 ] 4 f .
t ( x x , y y ) = const × exp { i k [ ( x x ) 2 + ( y y ) 2 ] 2 2 σ 3 } .

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