Abstract

An essential step in bispectral imaging is the recovery of the object’s Fourier phase from the bispectral phase. Such reconstruction can be performed by recursive or least-squares (minimization) methods. It is generally accepted that least-squares methods perform better because of their higher noise tolerance. Two weighted least-squares minimization schemes are compared, and the use of the error-reduction algorithm is suggested as a way to overcome the stagnation at local minima common to minimization problems.

© 1996 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. C. Daintyin Laser Speckle and Related Phenomena, J. C. Dainty, ed. (Springer-Verlag, Berlin, 1984), p. 259.
  2. A. W. Lohmann, G. Weigelt, B. WirnitzerAppl. Opt. 22, 4028 (1983).
    [CrossRef] [PubMed]
  3. G. R. Ayers, M. J. Northcott, J. C. DaintyJ. Opt. Soc. Am. A 5, 963 (1988).
    [CrossRef]
  4. P. W. Gorham, A. M. Ghez, S. R. Kulkarni, T. Nakajima, G. Neugebauer, J. B. Oke, T. A. PrinceAstron. J. 98, 1783 (1989).
    [CrossRef]
  5. C. A. HaniffJ. Opt. Soc. Am. A 8, 134 (1991).
    [CrossRef]
  6. A. Glindemann, R. G. Lane, J. C. Daintyin Digital Signal Processing ’91, V. Cappellini, A. G. Constantinides, ed. (Elsevier, Amsterdam, 1991), pp. 59-65.
  7. A. Glindemann, R. G. Lane, J. C. DaintyJ. Opt. Soc. Am. A 9, 543 (1992).
    [CrossRef]
  8. P. Negrete-Regagnon“Bispectral imaging in astronomy,” Ph.D. dissertation (Imperial College, London, 1995).
  9. The NAG fortran Library is available from NAG, Inc., Suite 200, 1400 Opus Place, Downers Grove, Ill. 60515-5702.
  10. J. R. FienupAppl. Opt. 21, 2758 (1982).
    [CrossRef] [PubMed]

1992

1991

1989

P. W. Gorham, A. M. Ghez, S. R. Kulkarni, T. Nakajima, G. Neugebauer, J. B. Oke, T. A. PrinceAstron. J. 98, 1783 (1989).
[CrossRef]

1988

1983

1982

Ayers, G. R.

Dainty, J. C.

A. Glindemann, R. G. Lane, J. C. DaintyJ. Opt. Soc. Am. A 9, 543 (1992).
[CrossRef]

G. R. Ayers, M. J. Northcott, J. C. DaintyJ. Opt. Soc. Am. A 5, 963 (1988).
[CrossRef]

J. C. Daintyin Laser Speckle and Related Phenomena, J. C. Dainty, ed. (Springer-Verlag, Berlin, 1984), p. 259.

A. Glindemann, R. G. Lane, J. C. Daintyin Digital Signal Processing ’91, V. Cappellini, A. G. Constantinides, ed. (Elsevier, Amsterdam, 1991), pp. 59-65.

Fienup, J. R.

Ghez, A. M.

P. W. Gorham, A. M. Ghez, S. R. Kulkarni, T. Nakajima, G. Neugebauer, J. B. Oke, T. A. PrinceAstron. J. 98, 1783 (1989).
[CrossRef]

Glindemann, A.

A. Glindemann, R. G. Lane, J. C. DaintyJ. Opt. Soc. Am. A 9, 543 (1992).
[CrossRef]

A. Glindemann, R. G. Lane, J. C. Daintyin Digital Signal Processing ’91, V. Cappellini, A. G. Constantinides, ed. (Elsevier, Amsterdam, 1991), pp. 59-65.

Gorham, P. W.

P. W. Gorham, A. M. Ghez, S. R. Kulkarni, T. Nakajima, G. Neugebauer, J. B. Oke, T. A. PrinceAstron. J. 98, 1783 (1989).
[CrossRef]

Haniff, C. A.

Kulkarni, S. R.

P. W. Gorham, A. M. Ghez, S. R. Kulkarni, T. Nakajima, G. Neugebauer, J. B. Oke, T. A. PrinceAstron. J. 98, 1783 (1989).
[CrossRef]

Lane, R. G.

A. Glindemann, R. G. Lane, J. C. DaintyJ. Opt. Soc. Am. A 9, 543 (1992).
[CrossRef]

A. Glindemann, R. G. Lane, J. C. Daintyin Digital Signal Processing ’91, V. Cappellini, A. G. Constantinides, ed. (Elsevier, Amsterdam, 1991), pp. 59-65.

Lohmann, A. W.

Nakajima, T.

P. W. Gorham, A. M. Ghez, S. R. Kulkarni, T. Nakajima, G. Neugebauer, J. B. Oke, T. A. PrinceAstron. J. 98, 1783 (1989).
[CrossRef]

Negrete-Regagnon, P.

P. Negrete-Regagnon“Bispectral imaging in astronomy,” Ph.D. dissertation (Imperial College, London, 1995).

Neugebauer, G.

P. W. Gorham, A. M. Ghez, S. R. Kulkarni, T. Nakajima, G. Neugebauer, J. B. Oke, T. A. PrinceAstron. J. 98, 1783 (1989).
[CrossRef]

Northcott, M. J.

Oke, J. B.

P. W. Gorham, A. M. Ghez, S. R. Kulkarni, T. Nakajima, G. Neugebauer, J. B. Oke, T. A. PrinceAstron. J. 98, 1783 (1989).
[CrossRef]

Prince, T. A.

P. W. Gorham, A. M. Ghez, S. R. Kulkarni, T. Nakajima, G. Neugebauer, J. B. Oke, T. A. PrinceAstron. J. 98, 1783 (1989).
[CrossRef]

Weigelt, G.

Wirnitzer, B.

Appl. Opt.

Astron. J.

P. W. Gorham, A. M. Ghez, S. R. Kulkarni, T. Nakajima, G. Neugebauer, J. B. Oke, T. A. PrinceAstron. J. 98, 1783 (1989).
[CrossRef]

J. Opt. Soc. Am. A

Other

P. Negrete-Regagnon“Bispectral imaging in astronomy,” Ph.D. dissertation (Imperial College, London, 1995).

The NAG fortran Library is available from NAG, Inc., Suite 200, 1400 Opus Place, Downers Grove, Ill. 60515-5702.

J. C. Daintyin Laser Speckle and Related Phenomena, J. C. Dainty, ed. (Springer-Verlag, Berlin, 1984), p. 259.

A. Glindemann, R. G. Lane, J. C. Daintyin Digital Signal Processing ’91, V. Cappellini, A. G. Constantinides, ed. (Elsevier, Amsterdam, 1991), pp. 59-65.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (2)

Fig. 1
Fig. 1

Illustration of the bispectral minimization and error-reduction iterative sequence. The images represent the modulo 2π difference between the original object Fourier phase and the reconstruction from processing 1000 computer-simulated speckle frames.

Fig. 2
Fig. 2

Performance comparison between objective functions E1 and E2.

Equations (8)

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

β ( u 1 , υ 1 , u 2 , υ 2 ) = ϕ ( u 1 , υ 1 ) + ϕ ( u 2 , υ 2 ) ϕ ( u 1 + u 2 , υ 1 + υ 2 ) .
E 1 = l = l min l max k = k min k max j = 1 n col i = 1 n row { mod [ β i j k l ( ϕ i j + ϕ k l ϕ i + k , j + l ) ] } 2 SNR i j k l β ,
E 2 = l = l min l max k = k min k max j = 1 n col i = 1 n row { [ Re ( Δ i j k l ) ] 2 + [ Im ( Δ i j k l ) ] 2 } SNR i j k l β ,
Δ i j k l = exp ( i β i j k l ) exp [ i ( ϕ i j + ϕ k l ϕ i + k , j + l ) ] ,
Re ( Δ i j k l ) = cos ( β i j k l ) cos ( ϕ i j + ϕ k l ϕ i + k , j + l ) ,
Im ( Δ i j k l ) = sin ( β i j k l ) sin ( ϕ i j + ϕ k l ϕ i + k , j + l ) .
E 1 ¯ = 2 l = l min l max k = k min k max { mod [ β m n k l ( ϕ m n + ϕ k l ϕ m + k , n + l ) ] } SNR m n k l β 2 j = 1 n col i = 1 n row { mod [ β i j m n ( ϕ i j + ϕ m n ϕ i + m , j + n ) ] } SNR i j m n β + 2 l = l min l max k = k min k max { mod [ β m k , n l , k , l ( ϕ m k , n l + ϕ k l ϕ m n ) ] } SNR m k , n l , k , l β ,
E 2 ϕ m n = l = l min l max k = k min k max [ 2 Re ( Δ m n k l ) sin ( ϕ m n + ϕ k l ϕ m + k , n + l ) 2 Im ( Δ m n k l ) cos ( ϕ m n + ϕ k l ϕ m + k , n + l ) ] SNR m n k l β + j = 1 n col i = 1 n row [ 2 Re ( Δ i j m n ) × sin ( ϕ i j + ϕ m n ϕ i + m , j + n ) 2 Im ( Δ i j m n ) × cos ( ϕ i j + ϕ m n ϕ i + m , j + n ) ] SNR i j m n β + l = l min l max k = k min k max [ 2 Im ( Δ m k , n l , k , l ) cos ( ϕ m k , n l + ϕ k l ϕ m n ) 2 Re ( Δ m k , n l , k , l ) × sin ( ϕ m k , n l + ϕ k l ϕ m n ) ] × SNR m k , n l , k , l β .

Metrics