Abstract

In a recent publication [ Appl. Opt. 42, 1932 ( 2003)], redundancies of phase-space representations were studied. In particular, signal recovery from a single section of the ambiguity function was explored. It is shown that this signal-recovery method can be associated with interferometry.

© 2005 Optical Society of America

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References

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  1. K. Vogel, H. Risken, “Determination of quasiprobability distributions in terms of probability distributions for the rotated quadrature phase,” Phys. Rev. A 40, 2847–2849 (1989).
    [CrossRef] [PubMed]
  2. M. G. Raymer, M. Beck, D. F. McAlister, “Complex wave-field reconstruction using phase-space tomography,” Phy. Rev. Lett. 72, 1137–1140 (1994).
    [CrossRef]
  3. D. Dragoman, M. Dragoman, K.-H. Brenner, “Tomographic amplitude and phase recovery of vertical-cavity surface-emitting lasers by use of the ambiguity function,” Opt. Lett. 27, 1519–1521 (2002).
    [CrossRef]
  4. D. Dragoman, “Redundancy of phase-space distribution functions in complex field recovery problems,” Appl. Opt. 42, 1932–1937 (2003).
    [CrossRef] [PubMed]
  5. T. Alieva, M. Bastiaans, L. Stanković, “Signal reconstruction from two close fractional Fourier power spectra,” IEEE Trans. Signal Process. 51, 112–123 (2003).
    [CrossRef]
  6. A. Semichaevsky, M. Testorf, “Phase-space interpretation of deterministic phase retrieval,” J. Opt. Soc. Am A 21, 2173–2179 (2004).
    [CrossRef]
  7. D. Malacara, M. Servín, Z. Malacara, Interferogram Analysis for Optical Testing (Marcel Dekker, New York, 1998), Chap. 1.6, pp. 13–21.
  8. C. Elster, “Exact two-dimensional wave-front reconstruction from lateral shearing interferograms with large shears,” Appl. Opt. 39, 5353–5359 (2000).
    [CrossRef]

2004

A. Semichaevsky, M. Testorf, “Phase-space interpretation of deterministic phase retrieval,” J. Opt. Soc. Am A 21, 2173–2179 (2004).
[CrossRef]

2003

T. Alieva, M. Bastiaans, L. Stanković, “Signal reconstruction from two close fractional Fourier power spectra,” IEEE Trans. Signal Process. 51, 112–123 (2003).
[CrossRef]

D. Dragoman, “Redundancy of phase-space distribution functions in complex field recovery problems,” Appl. Opt. 42, 1932–1937 (2003).
[CrossRef] [PubMed]

2002

2000

1994

M. G. Raymer, M. Beck, D. F. McAlister, “Complex wave-field reconstruction using phase-space tomography,” Phy. Rev. Lett. 72, 1137–1140 (1994).
[CrossRef]

1989

K. Vogel, H. Risken, “Determination of quasiprobability distributions in terms of probability distributions for the rotated quadrature phase,” Phys. Rev. A 40, 2847–2849 (1989).
[CrossRef] [PubMed]

Alieva, T.

T. Alieva, M. Bastiaans, L. Stanković, “Signal reconstruction from two close fractional Fourier power spectra,” IEEE Trans. Signal Process. 51, 112–123 (2003).
[CrossRef]

Bastiaans, M.

T. Alieva, M. Bastiaans, L. Stanković, “Signal reconstruction from two close fractional Fourier power spectra,” IEEE Trans. Signal Process. 51, 112–123 (2003).
[CrossRef]

Beck, M.

M. G. Raymer, M. Beck, D. F. McAlister, “Complex wave-field reconstruction using phase-space tomography,” Phy. Rev. Lett. 72, 1137–1140 (1994).
[CrossRef]

Brenner, K.-H.

Dragoman, D.

Dragoman, M.

Elster, C.

Malacara, D.

D. Malacara, M. Servín, Z. Malacara, Interferogram Analysis for Optical Testing (Marcel Dekker, New York, 1998), Chap. 1.6, pp. 13–21.

Malacara, Z.

D. Malacara, M. Servín, Z. Malacara, Interferogram Analysis for Optical Testing (Marcel Dekker, New York, 1998), Chap. 1.6, pp. 13–21.

McAlister, D. F.

M. G. Raymer, M. Beck, D. F. McAlister, “Complex wave-field reconstruction using phase-space tomography,” Phy. Rev. Lett. 72, 1137–1140 (1994).
[CrossRef]

Raymer, M. G.

M. G. Raymer, M. Beck, D. F. McAlister, “Complex wave-field reconstruction using phase-space tomography,” Phy. Rev. Lett. 72, 1137–1140 (1994).
[CrossRef]

Risken, H.

K. Vogel, H. Risken, “Determination of quasiprobability distributions in terms of probability distributions for the rotated quadrature phase,” Phys. Rev. A 40, 2847–2849 (1989).
[CrossRef] [PubMed]

Semichaevsky, A.

A. Semichaevsky, M. Testorf, “Phase-space interpretation of deterministic phase retrieval,” J. Opt. Soc. Am A 21, 2173–2179 (2004).
[CrossRef]

Servín, M.

D. Malacara, M. Servín, Z. Malacara, Interferogram Analysis for Optical Testing (Marcel Dekker, New York, 1998), Chap. 1.6, pp. 13–21.

Stankovic, L.

T. Alieva, M. Bastiaans, L. Stanković, “Signal reconstruction from two close fractional Fourier power spectra,” IEEE Trans. Signal Process. 51, 112–123 (2003).
[CrossRef]

Testorf, M.

A. Semichaevsky, M. Testorf, “Phase-space interpretation of deterministic phase retrieval,” J. Opt. Soc. Am A 21, 2173–2179 (2004).
[CrossRef]

Vogel, K.

K. Vogel, H. Risken, “Determination of quasiprobability distributions in terms of probability distributions for the rotated quadrature phase,” Phys. Rev. A 40, 2847–2849 (1989).
[CrossRef] [PubMed]

Appl. Opt.

IEEE Trans. Signal Process.

T. Alieva, M. Bastiaans, L. Stanković, “Signal reconstruction from two close fractional Fourier power spectra,” IEEE Trans. Signal Process. 51, 112–123 (2003).
[CrossRef]

J. Opt. Soc. Am A

A. Semichaevsky, M. Testorf, “Phase-space interpretation of deterministic phase retrieval,” J. Opt. Soc. Am A 21, 2173–2179 (2004).
[CrossRef]

Opt. Lett.

Phy. Rev. Lett.

M. G. Raymer, M. Beck, D. F. McAlister, “Complex wave-field reconstruction using phase-space tomography,” Phy. Rev. Lett. 72, 1137–1140 (1994).
[CrossRef]

Phys. Rev. A

K. Vogel, H. Risken, “Determination of quasiprobability distributions in terms of probability distributions for the rotated quadrature phase,” Phys. Rev. A 40, 2847–2849 (1989).
[CrossRef] [PubMed]

Other

D. Malacara, M. Servín, Z. Malacara, Interferogram Analysis for Optical Testing (Marcel Dekker, New York, 1998), Chap. 1.6, pp. 13–21.

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Equations (8)

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F ( r , r 0 ) = | u ( r + r 0 2 ) | | u ( r - r 0 2 ) | ,
G ( r , r 0 ) = exp [ i 2 ϕ ( r + r 0 2 ) - i 2 ϕ ( r - r 0 2 ) ] .
F ( r ) = u ( r ) 2 ,
G ( r , r 0 ) = exp [ i 2 r 0 ϕ ( r ) ] .
I g ( r ) = g ( r , r 0 ) 2 = | u ( r + r 0 2 ) | 2 + | u ( r - r 0 2 ) | 2 + 2 | u ( r + r 0 2 ) | × | u ( r - r 0 2 ) | cos [ ϕ ( r + r 0 2 ) - ϕ ( r - r 0 2 ) ] ,
I g ( r ) = 2 u ( r ) 2 { 1 + cos [ r 0 ϕ ( r ) ] } .
AF [ g ] ( r , p ) = 1 2 π - g ( r + r 2 , r 0 ) g * ( r - r 2 , r 0 ) exp ( i rp ) d 2 r = AF [ u ] ( r + r 0 , p ) + AF [ u ] ( r - r 0 , p ) + AF [ u ] ( r , p ) cos ( r 0 2 p ) .
AF [ g ] ( 0 , p ) = AF [ u ] ( r 0 , p ) + AF [ u ] ( - r 0 , p ) + AF [ u ] ( 0 , p ) cos ( r 0 2 p ) .

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