Abstract

We describe two different scale-tunable optical correlators working under totally incoherent light. They behave as spatially incoherent wavelength-independent imaging systems with an achromatic point-spread function (PSF). In both cases it is possible to adapt the scale of the achromatic PSF, i.e., to modify the scaling factor of the PSF and preserve the chromatic compensation, by one’s shifting the input along the optical axis. The remarkable properties of these systems allow us to carry out a scale-tunable color pattern-recognition experiment with natural light.

© 2001 Optical Society of America

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References

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  1. A. Vander Lugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theeory IF-10, 139–145 (1964).
    [CrossRef]
  2. H. J. Caulfield, R. Haimes, D. Casasent, “Beyond matched filtering,” Opt. Eng. 19, 152–156 (1980).
    [CrossRef]
  3. F. T. Gamble, L. M. Frye, D. R. Grieser, “Real-time fingerprint verification system,” Appl. Opt. 31, 652–655 (1992).
    [CrossRef] [PubMed]
  4. B. Javidi, J. L. Horner, “Optical pattern recognition for validation and security verification,” Opt. Eng. 33, 1752–1756 (1994).
    [CrossRef]
  5. A. Pu, R. Denkewalter, P. Psaltis, “Real-time vehicle navigation using a holographic memory,” Opt. Eng. 36, 2737–2746 (1997).
    [CrossRef]
  6. A. W. Lohmann, H. W. Werlich, “Incoherent matched filtering with Fourier holograms,” Appl. Opt. 10, 670–672 (1971).
    [CrossRef] [PubMed]
  7. J. van der Gracht, J. N. Mait, “Incoherent pattern recognition with phase-only filters,” Opt. Lett. 17, 1703–1705 (1992).
    [CrossRef] [PubMed]
  8. S. Gorodeisky, A. A. Friesem, “Phase filters for correlators with incoherent light,” Opt. Commun. 100, 421–425 (1993).
    [CrossRef]
  9. J. Ding, M. Itoh, T. Yatagai, “Optimal incoherent correlator for noisy gray-tone image recognition,” Opt. Lett. 20, 2411–2413 (1995).
    [CrossRef] [PubMed]
  10. J. D. Brasher, E. G. Johnson, “Incoherent optical correlators and phase encoding of identification codes for access control or authentification,” Opt. Eng. 36, 2409–2416 (1997).
    [CrossRef]
  11. G. M. Morris, D. A. Zweig, “White-light Fourier transformations,” in Optical Signal Processing, J. L. Horner, ed. (Academic, New York, 1987), Chap. 1.2.
  12. R. H. Katyl, “Compensating optical systems. 3: achromatic Fourier transformation,” Appl. Opt. 11, 1255–1260 (1972).
    [CrossRef] [PubMed]
  13. G. M. Morris, “Diffraction theory for an achromatic Fourier transformation,” Appl. Opt. 20, 2017–2025 (1981).
    [CrossRef] [PubMed]
  14. J. Lancis, P. Andrés, W. D. Furlan, A. Pons, “All-diffractive achromatic Fourier-transform setup,” Opt. Lett. 19, 402–404 (1994).
    [PubMed]
  15. E. Tajahuerce, V. Climent, J. Lancis, M. Fernández-Alonso, P. Andrés, “Achromatic Fourier transforming properties of a separated diffractive lens doublet: theory and experiment,” Appl. Opt. 37, 6164–6173 (1998).
    [CrossRef]
  16. J. Lancis, E. Tajahuerce, P. Andrés, G. Mínguez-Vega, M. Fernández-Alonso, V. Climent, “Quasi-wavelength-independent broadband optical Fourier transformer,” Opt. Commun. 172, 153–160 (1999).
    [CrossRef]
  17. G. M. Morris, “An ideal achromatic Fourier processor,” Opt. Commun. 39, 143–147 (1981).
    [CrossRef]
  18. R. Ferrière, C. Illueca, J. P. Goedgebuer, “Corrélateur achromatique bidimensionnel,” J. Opt. (Paris) 17, 153–159 (1986).
  19. E. Tajahuerce, J. Lancis, V. Climent, P. Andrés, “Hybrid (refractive–diffractive) Fourier processor: a novel optical architecture for achromatic processing with broadband point-source illumination,” Opt. Commun. 151, 86–92 (1998).
    [CrossRef]
  20. P. Andrés, V. Climent, J. Lancis, G. Mínguez-Vega, E. Tajahuerce, A. W. Lohmann, “All-incoherent dispersion-compensated optical correlator,” Opt. Lett. 24, 1331–1333 (1999).
    [CrossRef]
  21. A. Pe’er, D. Wang, A. W. Lohmann, A. A. Friesem, “Optical correlation with totally incoherent light,” Opt. Lett. 24, 1469–1471 (1999).
    [CrossRef]
  22. A. Pe’er, D. Wang, A. W. Lohmann, A. A. Firesem, “Apochromatic optical correlation,” Opt. Lett. 25, 776–778 (2000).
    [CrossRef]
  23. A. E. Siegman, Lasers (University Science Books, Mill Valley, Calif., 1986).
  24. A. Yariv, “Imaging of coherent fields through lenslike systems,” Opt. Lett. 19, 1607–1608 (1994).
    [CrossRef] [PubMed]
  25. M. T. Gale, M. Rosi, “Continuous-relief diffractive lenses and microlens arrays,” in Diffractive Optics for Industrial and Commercial Applications, J. Turunen, F. Wyrowsky, eds. (Akedemie Verlag, Berlin, 1997).

2000 (1)

1999 (3)

1998 (2)

E. Tajahuerce, V. Climent, J. Lancis, M. Fernández-Alonso, P. Andrés, “Achromatic Fourier transforming properties of a separated diffractive lens doublet: theory and experiment,” Appl. Opt. 37, 6164–6173 (1998).
[CrossRef]

E. Tajahuerce, J. Lancis, V. Climent, P. Andrés, “Hybrid (refractive–diffractive) Fourier processor: a novel optical architecture for achromatic processing with broadband point-source illumination,” Opt. Commun. 151, 86–92 (1998).
[CrossRef]

1997 (2)

J. D. Brasher, E. G. Johnson, “Incoherent optical correlators and phase encoding of identification codes for access control or authentification,” Opt. Eng. 36, 2409–2416 (1997).
[CrossRef]

A. Pu, R. Denkewalter, P. Psaltis, “Real-time vehicle navigation using a holographic memory,” Opt. Eng. 36, 2737–2746 (1997).
[CrossRef]

1995 (1)

1994 (3)

1993 (1)

S. Gorodeisky, A. A. Friesem, “Phase filters for correlators with incoherent light,” Opt. Commun. 100, 421–425 (1993).
[CrossRef]

1992 (2)

1986 (1)

R. Ferrière, C. Illueca, J. P. Goedgebuer, “Corrélateur achromatique bidimensionnel,” J. Opt. (Paris) 17, 153–159 (1986).

1981 (2)

1980 (1)

H. J. Caulfield, R. Haimes, D. Casasent, “Beyond matched filtering,” Opt. Eng. 19, 152–156 (1980).
[CrossRef]

1972 (1)

1971 (1)

1964 (1)

A. Vander Lugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theeory IF-10, 139–145 (1964).
[CrossRef]

Andrés, P.

J. Lancis, E. Tajahuerce, P. Andrés, G. Mínguez-Vega, M. Fernández-Alonso, V. Climent, “Quasi-wavelength-independent broadband optical Fourier transformer,” Opt. Commun. 172, 153–160 (1999).
[CrossRef]

P. Andrés, V. Climent, J. Lancis, G. Mínguez-Vega, E. Tajahuerce, A. W. Lohmann, “All-incoherent dispersion-compensated optical correlator,” Opt. Lett. 24, 1331–1333 (1999).
[CrossRef]

E. Tajahuerce, V. Climent, J. Lancis, M. Fernández-Alonso, P. Andrés, “Achromatic Fourier transforming properties of a separated diffractive lens doublet: theory and experiment,” Appl. Opt. 37, 6164–6173 (1998).
[CrossRef]

E. Tajahuerce, J. Lancis, V. Climent, P. Andrés, “Hybrid (refractive–diffractive) Fourier processor: a novel optical architecture for achromatic processing with broadband point-source illumination,” Opt. Commun. 151, 86–92 (1998).
[CrossRef]

J. Lancis, P. Andrés, W. D. Furlan, A. Pons, “All-diffractive achromatic Fourier-transform setup,” Opt. Lett. 19, 402–404 (1994).
[PubMed]

Brasher, J. D.

J. D. Brasher, E. G. Johnson, “Incoherent optical correlators and phase encoding of identification codes for access control or authentification,” Opt. Eng. 36, 2409–2416 (1997).
[CrossRef]

Casasent, D.

H. J. Caulfield, R. Haimes, D. Casasent, “Beyond matched filtering,” Opt. Eng. 19, 152–156 (1980).
[CrossRef]

Caulfield, H. J.

H. J. Caulfield, R. Haimes, D. Casasent, “Beyond matched filtering,” Opt. Eng. 19, 152–156 (1980).
[CrossRef]

Climent, V.

J. Lancis, E. Tajahuerce, P. Andrés, G. Mínguez-Vega, M. Fernández-Alonso, V. Climent, “Quasi-wavelength-independent broadband optical Fourier transformer,” Opt. Commun. 172, 153–160 (1999).
[CrossRef]

P. Andrés, V. Climent, J. Lancis, G. Mínguez-Vega, E. Tajahuerce, A. W. Lohmann, “All-incoherent dispersion-compensated optical correlator,” Opt. Lett. 24, 1331–1333 (1999).
[CrossRef]

E. Tajahuerce, J. Lancis, V. Climent, P. Andrés, “Hybrid (refractive–diffractive) Fourier processor: a novel optical architecture for achromatic processing with broadband point-source illumination,” Opt. Commun. 151, 86–92 (1998).
[CrossRef]

E. Tajahuerce, V. Climent, J. Lancis, M. Fernández-Alonso, P. Andrés, “Achromatic Fourier transforming properties of a separated diffractive lens doublet: theory and experiment,” Appl. Opt. 37, 6164–6173 (1998).
[CrossRef]

Denkewalter, R.

A. Pu, R. Denkewalter, P. Psaltis, “Real-time vehicle navigation using a holographic memory,” Opt. Eng. 36, 2737–2746 (1997).
[CrossRef]

Ding, J.

Fernández-Alonso, M.

J. Lancis, E. Tajahuerce, P. Andrés, G. Mínguez-Vega, M. Fernández-Alonso, V. Climent, “Quasi-wavelength-independent broadband optical Fourier transformer,” Opt. Commun. 172, 153–160 (1999).
[CrossRef]

E. Tajahuerce, V. Climent, J. Lancis, M. Fernández-Alonso, P. Andrés, “Achromatic Fourier transforming properties of a separated diffractive lens doublet: theory and experiment,” Appl. Opt. 37, 6164–6173 (1998).
[CrossRef]

Ferrière, R.

R. Ferrière, C. Illueca, J. P. Goedgebuer, “Corrélateur achromatique bidimensionnel,” J. Opt. (Paris) 17, 153–159 (1986).

Firesem, A. A.

Friesem, A. A.

A. Pe’er, D. Wang, A. W. Lohmann, A. A. Friesem, “Optical correlation with totally incoherent light,” Opt. Lett. 24, 1469–1471 (1999).
[CrossRef]

S. Gorodeisky, A. A. Friesem, “Phase filters for correlators with incoherent light,” Opt. Commun. 100, 421–425 (1993).
[CrossRef]

Frye, L. M.

Furlan, W. D.

Gale, M. T.

M. T. Gale, M. Rosi, “Continuous-relief diffractive lenses and microlens arrays,” in Diffractive Optics for Industrial and Commercial Applications, J. Turunen, F. Wyrowsky, eds. (Akedemie Verlag, Berlin, 1997).

Gamble, F. T.

Goedgebuer, J. P.

R. Ferrière, C. Illueca, J. P. Goedgebuer, “Corrélateur achromatique bidimensionnel,” J. Opt. (Paris) 17, 153–159 (1986).

Gorodeisky, S.

S. Gorodeisky, A. A. Friesem, “Phase filters for correlators with incoherent light,” Opt. Commun. 100, 421–425 (1993).
[CrossRef]

Grieser, D. R.

Haimes, R.

H. J. Caulfield, R. Haimes, D. Casasent, “Beyond matched filtering,” Opt. Eng. 19, 152–156 (1980).
[CrossRef]

Horner, J. L.

B. Javidi, J. L. Horner, “Optical pattern recognition for validation and security verification,” Opt. Eng. 33, 1752–1756 (1994).
[CrossRef]

Illueca, C.

R. Ferrière, C. Illueca, J. P. Goedgebuer, “Corrélateur achromatique bidimensionnel,” J. Opt. (Paris) 17, 153–159 (1986).

Itoh, M.

Javidi, B.

B. Javidi, J. L. Horner, “Optical pattern recognition for validation and security verification,” Opt. Eng. 33, 1752–1756 (1994).
[CrossRef]

Johnson, E. G.

J. D. Brasher, E. G. Johnson, “Incoherent optical correlators and phase encoding of identification codes for access control or authentification,” Opt. Eng. 36, 2409–2416 (1997).
[CrossRef]

Katyl, R. H.

Lancis, J.

P. Andrés, V. Climent, J. Lancis, G. Mínguez-Vega, E. Tajahuerce, A. W. Lohmann, “All-incoherent dispersion-compensated optical correlator,” Opt. Lett. 24, 1331–1333 (1999).
[CrossRef]

J. Lancis, E. Tajahuerce, P. Andrés, G. Mínguez-Vega, M. Fernández-Alonso, V. Climent, “Quasi-wavelength-independent broadband optical Fourier transformer,” Opt. Commun. 172, 153–160 (1999).
[CrossRef]

E. Tajahuerce, J. Lancis, V. Climent, P. Andrés, “Hybrid (refractive–diffractive) Fourier processor: a novel optical architecture for achromatic processing with broadband point-source illumination,” Opt. Commun. 151, 86–92 (1998).
[CrossRef]

E. Tajahuerce, V. Climent, J. Lancis, M. Fernández-Alonso, P. Andrés, “Achromatic Fourier transforming properties of a separated diffractive lens doublet: theory and experiment,” Appl. Opt. 37, 6164–6173 (1998).
[CrossRef]

J. Lancis, P. Andrés, W. D. Furlan, A. Pons, “All-diffractive achromatic Fourier-transform setup,” Opt. Lett. 19, 402–404 (1994).
[PubMed]

Lohmann, A. W.

Mait, J. N.

Mínguez-Vega, G.

J. Lancis, E. Tajahuerce, P. Andrés, G. Mínguez-Vega, M. Fernández-Alonso, V. Climent, “Quasi-wavelength-independent broadband optical Fourier transformer,” Opt. Commun. 172, 153–160 (1999).
[CrossRef]

P. Andrés, V. Climent, J. Lancis, G. Mínguez-Vega, E. Tajahuerce, A. W. Lohmann, “All-incoherent dispersion-compensated optical correlator,” Opt. Lett. 24, 1331–1333 (1999).
[CrossRef]

Morris, G. M.

G. M. Morris, “An ideal achromatic Fourier processor,” Opt. Commun. 39, 143–147 (1981).
[CrossRef]

G. M. Morris, “Diffraction theory for an achromatic Fourier transformation,” Appl. Opt. 20, 2017–2025 (1981).
[CrossRef] [PubMed]

G. M. Morris, D. A. Zweig, “White-light Fourier transformations,” in Optical Signal Processing, J. L. Horner, ed. (Academic, New York, 1987), Chap. 1.2.

Pe’er, A.

Pons, A.

Psaltis, P.

A. Pu, R. Denkewalter, P. Psaltis, “Real-time vehicle navigation using a holographic memory,” Opt. Eng. 36, 2737–2746 (1997).
[CrossRef]

Pu, A.

A. Pu, R. Denkewalter, P. Psaltis, “Real-time vehicle navigation using a holographic memory,” Opt. Eng. 36, 2737–2746 (1997).
[CrossRef]

Rosi, M.

M. T. Gale, M. Rosi, “Continuous-relief diffractive lenses and microlens arrays,” in Diffractive Optics for Industrial and Commercial Applications, J. Turunen, F. Wyrowsky, eds. (Akedemie Verlag, Berlin, 1997).

Siegman, A. E.

A. E. Siegman, Lasers (University Science Books, Mill Valley, Calif., 1986).

Tajahuerce, E.

J. Lancis, E. Tajahuerce, P. Andrés, G. Mínguez-Vega, M. Fernández-Alonso, V. Climent, “Quasi-wavelength-independent broadband optical Fourier transformer,” Opt. Commun. 172, 153–160 (1999).
[CrossRef]

P. Andrés, V. Climent, J. Lancis, G. Mínguez-Vega, E. Tajahuerce, A. W. Lohmann, “All-incoherent dispersion-compensated optical correlator,” Opt. Lett. 24, 1331–1333 (1999).
[CrossRef]

E. Tajahuerce, J. Lancis, V. Climent, P. Andrés, “Hybrid (refractive–diffractive) Fourier processor: a novel optical architecture for achromatic processing with broadband point-source illumination,” Opt. Commun. 151, 86–92 (1998).
[CrossRef]

E. Tajahuerce, V. Climent, J. Lancis, M. Fernández-Alonso, P. Andrés, “Achromatic Fourier transforming properties of a separated diffractive lens doublet: theory and experiment,” Appl. Opt. 37, 6164–6173 (1998).
[CrossRef]

van der Gracht, J.

Vander Lugt, A.

A. Vander Lugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theeory IF-10, 139–145 (1964).
[CrossRef]

Wang, D.

Werlich, H. W.

Yariv, A.

Yatagai, T.

Zweig, D. A.

G. M. Morris, D. A. Zweig, “White-light Fourier transformations,” in Optical Signal Processing, J. L. Horner, ed. (Academic, New York, 1987), Chap. 1.2.

Appl. Opt. (5)

IEEE Trans. Inf. Theeory (1)

A. Vander Lugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theeory IF-10, 139–145 (1964).
[CrossRef]

J. Opt. (Paris) (1)

R. Ferrière, C. Illueca, J. P. Goedgebuer, “Corrélateur achromatique bidimensionnel,” J. Opt. (Paris) 17, 153–159 (1986).

Opt. Commun. (4)

E. Tajahuerce, J. Lancis, V. Climent, P. Andrés, “Hybrid (refractive–diffractive) Fourier processor: a novel optical architecture for achromatic processing with broadband point-source illumination,” Opt. Commun. 151, 86–92 (1998).
[CrossRef]

S. Gorodeisky, A. A. Friesem, “Phase filters for correlators with incoherent light,” Opt. Commun. 100, 421–425 (1993).
[CrossRef]

J. Lancis, E. Tajahuerce, P. Andrés, G. Mínguez-Vega, M. Fernández-Alonso, V. Climent, “Quasi-wavelength-independent broadband optical Fourier transformer,” Opt. Commun. 172, 153–160 (1999).
[CrossRef]

G. M. Morris, “An ideal achromatic Fourier processor,” Opt. Commun. 39, 143–147 (1981).
[CrossRef]

Opt. Eng. (4)

H. J. Caulfield, R. Haimes, D. Casasent, “Beyond matched filtering,” Opt. Eng. 19, 152–156 (1980).
[CrossRef]

B. Javidi, J. L. Horner, “Optical pattern recognition for validation and security verification,” Opt. Eng. 33, 1752–1756 (1994).
[CrossRef]

A. Pu, R. Denkewalter, P. Psaltis, “Real-time vehicle navigation using a holographic memory,” Opt. Eng. 36, 2737–2746 (1997).
[CrossRef]

J. D. Brasher, E. G. Johnson, “Incoherent optical correlators and phase encoding of identification codes for access control or authentification,” Opt. Eng. 36, 2409–2416 (1997).
[CrossRef]

Opt. Lett. (7)

Other (3)

M. T. Gale, M. Rosi, “Continuous-relief diffractive lenses and microlens arrays,” in Diffractive Optics for Industrial and Commercial Applications, J. Turunen, F. Wyrowsky, eds. (Akedemie Verlag, Berlin, 1997).

A. E. Siegman, Lasers (University Science Books, Mill Valley, Calif., 1986).

G. M. Morris, D. A. Zweig, “White-light Fourier transformations,” in Optical Signal Processing, J. L. Horner, ed. (Academic, New York, 1987), Chap. 1.2.

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Figures (6)

Fig. 1
Fig. 1

Three-lens scale-tunable optical correlator that uses natural light.

Fig. 2
Fig. 2

Dimensionless scale parameter γ r (solid curve) and the position of the aperture D 0′ (dashed curve) plotted versus the position of the input z. It is assumed that Z 0 = 200 mm and σ C = 1.77 µm-1.

Fig. 3
Fig. 3

Totally incoherent optical correlator with linearly variable scale.

Fig. 4
Fig. 4

SCE plotted versus σ associated with the incoherent PSF of the optical setup of Fig. 3 for two different input locations: z = ∞ (long-dashed curve) and z = d (short-dashed curve). The SCE associated with the PSF of a conventional processor is represented by the solid curve.

Fig. 5
Fig. 5

Black-and-white image of the input object used in the correlation experiment. The object consisted of a set of colored alphabetical letters. From left to right and top to bottom the character colors were blue, red, green and gray.

Fig. 6
Fig. 6

Result of the color pattern-recognition experiment showing gray-level images of the irradiance distribution at the output plane of the system shown in Fig. 1 with a single matched filter for the character A for two different positions of the input object: (a) The system was adapted to recognize the small-sized letter A. (b) The system was adapted to recognized the large-sized letter A. The color of each peak is the same as the color of the corresponding character shown in Fig. 5.

Equations (36)

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Uoutx, y; σ=expiπσ DBx2+y2×-  Uinx, y; σexpiπσ ABx2+y2×exp-i2πσBxx+yydxdy,
Uoutx, y; σ=expiπσ CAx2+y2UinxA, yA; σ.
ABCD=1I00110-1/Z211l0110-1/f1×1l0110-1/Z111z01,
1l+1l=1f,  Z0=-M2Z0,
I0=-MM0z,
Ioutx, y; σ=txM0, yM02.
sσ=D0-σ0Z0σ-1z-1.
ABCD=1I00110-1/Z211l0110-1/f1×1l-D001101/sσ1.
hx, y; σ=p˜xβσ, yβσ2,
βσ=Bσσ=M0D0zσ0Z0σ2-D0+zσ.
βσσσ0=0,
D0=zZ02z-Z0.
β0=-z2σ02z-Z0 M0=γM0,
γ=-z2σ02z-Z0.
Ioutx, y=IinxM0, yM0*p˜xM0γ, yM0γ2,
px, y=Ĩtar*xMp, yMp,
Ioutx, y=IinxM0, yM0*Itar-MpxM0γ-MpyM0γ.
Mp=γMr.
z=MpMrσ0-1±1-1MpMrZ0σ01/2.
ABCD=1I00110-1/Z411l201×10-1/f211e-l0110-1/Z31×1l0110-1/f111l0110-1/Z21×1d0110-1/Z111z-d01,
1l+1l=1f1,  Z0=-M2Z0,
-1d+l-f1e/e+1l2+f2e/e=-tf1f2,  Z0=-M1/2Z0,
I0=-MM0z-d.
ABCD=1I00110-1/Z411l20110-1/f21×1e-l0110-1/Z31×1l01×10-1/f111l-D001101/sσ1,
sσ=D0-Z0σσ0-σZ0d-σ0Z0σ-1z-d-1-1,
Bσ=M0σ2Z0Z0(dσ0D0σ0d-z+σZ0z-D0-d+σD0σ0zZ0+Z0-σZ0Z0-σzZ0Z0).
d=-Z0Z01/2,
D0=-d2d+2Z0.
βσ=σ-σ02d2-dz+σσ0-2σzZ0σ3d+2Z0 M0.
β0=βσ0=-Z0zσ0d+2Z0 M0=γM0,
γ=-Z0zσ0d+2Z0.
z=d+2Z0σ0Z0 MpMr,
SCEσ=100 β0-βσβ0,
SCEσ=100 σ-σ02d2σ0-dσ0z+σzZ0σ3zZ0.
SCEσ=100 σ-σ02σ2for z=d100 σ-σ02σ2σZ0-dσ0σZ0for z.
SCEσ=100 σ-σ0σ.

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