Abstract

We demonstrate a novel method to enhance the phase resolution of a barium titanate beam-fanning novelty filter by means of an external phase shift in one part of the signal wave. The new technique is described theoretically on the basis of the coupled-wave theory. Experimental results are presented to demonstrate the behavior and the advantages of the novel device for the evaluation of spatial and temporal phase changes in incident signal waves.

© 1995 Optical Society of America

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References

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  1. D. Z. Anderson, J. Feinberg, “Optical novelty filters,” IEEE J. Quantum Electron. 25, 635–647 (1989).
    [CrossRef]
  2. J. E. Ford, Y. Fainman, H. S. Lee, “Time-integrating interferometry using photorefractive fanout,” Opt. Lett. 13, 856–858 (1988).
    [CrossRef] [PubMed]
  3. H. Rehn, R. Kowarschik, K. H. Ringhofer, “Transient phase detection with barium titanate novelty filters,” in 16th Congress of the International Commission for Optics: Optics as a Key to High Technology, G. Ákos, T. Lippényi, G. Lupkovics, A. Podmaniczky, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1983, 843–844 (1993).
  4. M. Segev, D. Engin, A. Yariv, G. C. Valley, “Temporal evolution of fanning in photorefractive materials,” Opt. Lett. 18, 956–961 (1993).
    [CrossRef] [PubMed]
  5. Transverse phase variations that are due to wave coupling are obtained when Eqs. (1) and (3) are solved.
  6. H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).
  7. P. Refregier, L. Solymar, H. Rajbenbach, J.-P. Huignard, “Two-beam coupling in photorefractive Bi12SiO20 crystals with moving grating: theory and experiments,” J. Appl. Phys. 58, 45–57 (1985).
    [CrossRef]

1993 (1)

1989 (1)

D. Z. Anderson, J. Feinberg, “Optical novelty filters,” IEEE J. Quantum Electron. 25, 635–647 (1989).
[CrossRef]

1988 (1)

1985 (1)

P. Refregier, L. Solymar, H. Rajbenbach, J.-P. Huignard, “Two-beam coupling in photorefractive Bi12SiO20 crystals with moving grating: theory and experiments,” J. Appl. Phys. 58, 45–57 (1985).
[CrossRef]

1969 (1)

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

Anderson, D. Z.

D. Z. Anderson, J. Feinberg, “Optical novelty filters,” IEEE J. Quantum Electron. 25, 635–647 (1989).
[CrossRef]

Engin, D.

Fainman, Y.

Feinberg, J.

D. Z. Anderson, J. Feinberg, “Optical novelty filters,” IEEE J. Quantum Electron. 25, 635–647 (1989).
[CrossRef]

Ford, J. E.

Huignard, J.-P.

P. Refregier, L. Solymar, H. Rajbenbach, J.-P. Huignard, “Two-beam coupling in photorefractive Bi12SiO20 crystals with moving grating: theory and experiments,” J. Appl. Phys. 58, 45–57 (1985).
[CrossRef]

Kogelnik, H.

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

Kowarschik, R.

H. Rehn, R. Kowarschik, K. H. Ringhofer, “Transient phase detection with barium titanate novelty filters,” in 16th Congress of the International Commission for Optics: Optics as a Key to High Technology, G. Ákos, T. Lippényi, G. Lupkovics, A. Podmaniczky, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1983, 843–844 (1993).

Lee, H. S.

Rajbenbach, H.

P. Refregier, L. Solymar, H. Rajbenbach, J.-P. Huignard, “Two-beam coupling in photorefractive Bi12SiO20 crystals with moving grating: theory and experiments,” J. Appl. Phys. 58, 45–57 (1985).
[CrossRef]

Refregier, P.

P. Refregier, L. Solymar, H. Rajbenbach, J.-P. Huignard, “Two-beam coupling in photorefractive Bi12SiO20 crystals with moving grating: theory and experiments,” J. Appl. Phys. 58, 45–57 (1985).
[CrossRef]

Rehn, H.

H. Rehn, R. Kowarschik, K. H. Ringhofer, “Transient phase detection with barium titanate novelty filters,” in 16th Congress of the International Commission for Optics: Optics as a Key to High Technology, G. Ákos, T. Lippényi, G. Lupkovics, A. Podmaniczky, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1983, 843–844 (1993).

Ringhofer, K. H.

H. Rehn, R. Kowarschik, K. H. Ringhofer, “Transient phase detection with barium titanate novelty filters,” in 16th Congress of the International Commission for Optics: Optics as a Key to High Technology, G. Ákos, T. Lippényi, G. Lupkovics, A. Podmaniczky, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1983, 843–844 (1993).

Segev, M.

Solymar, L.

P. Refregier, L. Solymar, H. Rajbenbach, J.-P. Huignard, “Two-beam coupling in photorefractive Bi12SiO20 crystals with moving grating: theory and experiments,” J. Appl. Phys. 58, 45–57 (1985).
[CrossRef]

Valley, G. C.

Yariv, A.

Bell Syst. Tech. J. (1)

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

IEEE J. Quantum Electron. (1)

D. Z. Anderson, J. Feinberg, “Optical novelty filters,” IEEE J. Quantum Electron. 25, 635–647 (1989).
[CrossRef]

J. Appl. Phys. (1)

P. Refregier, L. Solymar, H. Rajbenbach, J.-P. Huignard, “Two-beam coupling in photorefractive Bi12SiO20 crystals with moving grating: theory and experiments,” J. Appl. Phys. 58, 45–57 (1985).
[CrossRef]

Opt. Lett. (2)

Other (2)

Transverse phase variations that are due to wave coupling are obtained when Eqs. (1) and (3) are solved.

H. Rehn, R. Kowarschik, K. H. Ringhofer, “Transient phase detection with barium titanate novelty filters,” in 16th Congress of the International Commission for Optics: Optics as a Key to High Technology, G. Ákos, T. Lippényi, G. Lupkovics, A. Podmaniczky, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1983, 843–844 (1993).

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Figures (7)

Fig. 1
Fig. 1

Ordinary beam-fanning novelty filter.

Fig. 2
Fig. 2

Diagram of the split signal wave (signal part S and internal reference part Sref), the scattered fanout wave F, and the coordinate system.

Fig. 3
Fig. 3

Diagram of the mode of operation of the beam-fanning novelty filter with an enhanced phase resolution.

Fig. 4
Fig. 4

Experimental arrangement of the beam-fanning novelty filter with enhanced phase resolution.

Fig. 5
Fig. 5

Theoretically and experimentally measured dependences of the novelty contrast on the applied phase shift.

Fig. 6
Fig. 6

Periodic phase structure appearing in the signal wave. Enhanced dynamic phase resolution that is due to the additional phase shift.

Fig. 7
Fig. 7

Phase visualization by means of the developed phase-resolution-enhancement method. Investigation of turbulence caused by a stream of hot air (v ≈ 10 cm s−1) directed to the lower side of a cylindrical test object. (a) Visualization with an ordinary beam-fanning novelty filter, and (b) the higher contrast for visualization with the help of an additional phase shift.

Equations (26)

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S z = - α S - κ Γ F ,
τ Γ ˙ + Γ = 2 S F * S S * + F F *
F x = - α F + κ Γ * S .
F ( x = 0 , z ) = S ( x = 0 , z ) M .
S z = - α S - 2 κ S F 2 S 2 + F 2 - ( α + 2 κ M 2 + 1 ) S ,
S ( z ) = S ( z = 0 ) exp [ - ( α + δ ) z ] ,
δ = 2 κ M 2 + 1 .
S ref ( z , t > 0 ) = S ref ( z , t = 0 ) exp ( - i ϕ 0 ) = S s ( z ) exp ( - i ϕ 0 ) .
F ( x = 0 , z , t > 0 ) = S s ( z ) M exp ( - i ϕ 0 ) .
S z = - α S - κ Γ s F - α S - δ S s exp ( - i ϕ 0 )
S ( z ) = S ( 0 ) exp ( - α z ) + S s ( 0 ) exp ( - i ϕ 0 ) × exp ( - α z ) [ exp ( - δ z ) - 1 ] .
G ( z ) = S ( z ) S * ( z ) S ( 0 ) S * ( 0 )
G ( z , ϕ 0 ) = exp ( - 2 α z ) { 1 + [ exp ( - δ z ) - 1 ] 2 + 2 cos ϕ 0 [ exp ( - δ z ) - 1 ] } .
c N ( z , ϕ 0 ) = G ( z , ϕ 0 ) G ( z , 0 ) = 1 + V ( z ) ( 1 - cos ϕ 0 ) ,
V ( z ) = 2 exp ( δ z ) [ exp ( δ z ) - 1 ] .
Q N ( z ) = c N ( z ) ϕ 0 = V ( z ) sin ϕ 0 .
F s x = 2 κ S s 2 F s S s 2 + F s 2 ,
ln [ F s ( x ) F s ( 0 ) ] + 1 2 M 2 [ F s 2 ( x ) F s 2 ( 0 ) - 1 ] = 2 κ x ,
F x = - α F + F s x S S s ,
F ( x ) = exp ( - α x ) S S s 0 x F s x exp ( α x ) d x + F s ( 0 ) exp ( - i ϕ 0 - α x ) .
F ( x ) = S S s { F s ( x ) - F s ( 0 ) exp ( - α x ) - α × 0 x F s ( x ) exp [ α ( x - x ) ] d x } + F s ( 0 ) exp ( - i φ 0 - α x ) .
tan ϕ ( x ) = F s ( 0 ) sin ϕ 0 F s ( x ) exp ( α x ) - F s ( 0 ) + F s ( 0 ) cos ϕ 0 ,
tan ϕ 0 2 = sin ϕ 0 1 + cos ϕ 0 ,
F s ( x H ) F s ( 0 ) = 2 exp ( - α x H ) .
x H = ln 2 2 κ ,
κ = π n eo 3 r 42 cos η sin 2 η cos 2 θ e λ 2 4 π n eo sin θ k B T + 4 π n eo 0 ( η ) e N A sin θ .

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